How do concordats mesh with a country's laws? Legal experts explain
In (monist) countries where international treaties are at the top of a single hierarchy of laws, concordats have automatic precedence even over constitutions. In dualist countries, on the other hand, concordats must be incorporated into national law and their priority varies, though, even here concordats generally outweigh national laws.
Below are three excerpts about the interface between concordats and a country's constitution and national laws.
♦ The first explains the different legal frameworks, monist and dualist, which, in theory affect "the steps that are needed before an international treaty is to have effect within a national system of law and what a court is to do in a situation where the obligations under international and national law differ".
♦ The second excerpt, from legal scholar Alfred de Zayas, indicates the different priorities given in different countries to a UN human rights treaty (which is what concordats purport to be).
♦ And the third excerpt, from EU human rights experts, notes the varying legal weight accorded to Vatican concordats in Italy, France, Portugal and Spain.
Theories of incorporation and the constitutional context
Simon S C Tay 
Source: The Singapore Legal System and International Law:
Influence or Interference, pp. 471-73
Theories of how the international law system intersects with national systems are divided between the monist and dualist schools of jurisprudence. The monist holds that there is just one legal system, incorporating both international and national (or municipal) levels. The dualist holds that there are separate legal systems international and national (or municipal) levels.
The difference between theories relates, on a practical level, to the steps that are needed before an international treaty is to have effect within a national system of law and what a court is to do in a situation where the obligations under international and national law differ.
The monist requires that the two systems be unified. [...] Most monists argue that municipal or national law must be subordinated to international law and conform to its requirements. In some national legal systems, there are constitutional or other provisions that integrate international law, creating rights and duties for citizens, and hold international law to be supreme over national law. It would then be open for courts to refer to those international laws in priority over national laws. Such a legal system creates a single, monistic structure of law in which international law is incorporated without corresponding national legislation; or in which it can even override national laws.
On the other hand, dualists generally assume that international and national legal systems are separate and have no direct relationship to each other. Such a view creates the possibility of conflict between systems. Both may have legislated on the same matter and come to different provisions. The conflict, however, may be limited. Fitzmaurice’s suggestion is that dualism creates no conflict of laws but, at most, a conflict of obligations for the state. That is to say, where the state follows municipal or national law over international law, it is answerable to the international community for a breach of international obligations. There is, however, no breach of national obligations and no wrong to its citizens. In this view, no citizen can refer directly to an international treaty for a right against his or her government. Similarly, no duty is directly imposed on citizens by international law.
For dualists, a necessary and prior step is that the legislature must pass legislation incorporating international treaties into the national legal system. Where the state does not do so, it remains unincorporated in the national system, although the state may have ratified that international treaty. Such a treaty cannot generally be referred to by the Courts or be given precedence over national laws.
In addition to the difference between dualist and monist views, some jurisdictions, such as the United States, have drawn a distinction between self-executing treaties and non-self-executing treaties. There is some (but not exact) correspondence of these terms to the distinction between monist and dualist. Where a treaty is non-self-executing, there needs to be further legislation by the national legislature. This can be given or denied. Where the treaty is self-executing, no further legislation is needed to give it effect within the national legal system. Self-executing treaties, as such, yield the same result as the monist theory and would seem to place less emphasis on the legislature as the essential source of law in the national legal system. The concept of self-executing treaties can, however, be supported by the American constitution which includes international law as part of the law of the land. Additionally, the practice of the American system to include the legislature in the process of treaty-making and ratification, and not just the executive as is commonly the practice in other states. By such participation, [the] legislature retains its powers to adopt or reject international law. […]
The English system [has] been labelled “radically” dualist for its tendency not to incorporate or even refer to international law directly. […] An international treaty must first be incorporated into [national] law before that treaty has effect in the national system. […] The British practice [allows] the executive to act as the primary institution in treaty-making. Unlike the United States, there is no need for the legislature to decide on the ratification of a treaty; the conduct of foreign relations and the acceptance of international law treaties is very much the prerogative of the executive. However, international treaties cannot be incorporated into national law without corresponding national laws. This normally requires the concurrence of the legislature to the new laws. In this way, the primary role of the legislature in law-making is preserved.
The general constitutional scheme, as such, is one of segregation between international and national laws, and of the institutions of state that are responsible for them. The executive are responsible for foreign policy and international commitments, including the conclusion of treaties which may create international obligations. They may do this without prior reference to the legislature. The legislature, on the other hand, is responsible for national law-making. The legislature is under no constitutional obligation to pass laws pursuant to or even consistent with any international obligations the executive has undertaken.
Constitutional rights and the internationalisation of human rights
Alfred de Zayas 
Source: “Le Droit Constitutionnel Et L'internationalisation Des Droits De L'homme”
Legal priority is given to international treaties in most, but not all countries of the world. Exactly how the weight accorded to treaties varies from country to country is set out below. The legal scholar, Alfred de Zayas, sketches the different priorities given to a UN human rights treaty in different countries. This framework will not apply to concordats in those few countries like Italy where the constitution itself refers to a concordat. However, it should suffice to give a general idea of the great weight accorded to concordats.
The treaty forms part of the internal law of more than 80 member states. In Spain and in the Netherlands, the treaty has precedence over the Constitution.
In Armenia, Panama, Rwanda and Venezuela, the treaty carries equal weight with the Constitution.
In some 50 states, the Agreement does not have constitutional status, but has more force than national law, for example in Chile, France, Italy, Peru, Rwanda, Switzerland and Togo.
In some 15 states, the Agreement has the same force as national law, for example in Bolivia, Egypt, Finland, Germany, Hungary, Iraq, Iran, Lebanon, Mexico, the Republic of Korea, the former Yugoslav republic of Macedonia and of Uruguay. 
Legal ranking of concordats in some European states
EU Network of Independent Experts on Fundamental Rights
Source: Opinion N° 4-2005 by the EU Network of Independent Experts on Fundamental Rights, p. 6 
A precise description of the ranking of a concordat in various legal frameworks is given below for Italy, France, Portugal and Spain.
In certain Member States, international treaties are recognized [as having] primacy above all national laws, including the national Constitution.
In the case of Italy, this is in practice the status which is recognized to the 1929 Lateran Pacts between the Holy See and the State, as Article 7 of the Constitution envisages explicitly that the relationship between the government and the Catholic Church is regulated by those pacts signed in 1929. Amendments to these pacts which are accepted by both parties, however, do not require the procedure of constitutional amendments: such has been the case, in particular, of the Accord between the Republic of Italy and the Holy See of 18 February 1984, which substantially revised the Agreement of 1929.
In other Member States, they are recognized [as having] primacy only above legislation, but not above the Constitution.
France belongs to this second category of States. As a result, if concluded with France, a concordat […] would only be applicable to the extent that it would be compatible with the principles of equality and of secularism (laïcité), as enshrined respectively in Art. 1 of the [Declaration of the Rights of Man and of the Citizen] (equality) and in both Art. 10 of this Declaration and in the Preamble of the Constitution of 27 October 1946 (secularism). It is doubtful that this would indeed be the case. […]
In Portugal also, international treaties are not recognized [as having] primacy above the Constitution.
Similarly in Spain, international treaties may only be ratified after an amendment to the Constitution, where an incompatibility is identified by the Constitutional Court (Art. 95 of the Constitution), implying that the Constitution remains the supreme law of the land. 
1. Simon S C Tay, "The Singapore Legal System and International Law: Influence or Interference" (pp. 467-495) in Kevin Y L Tan, ed., The Singapore legal system, Singapore University Press, Second Edition, 1999, pp. 471-73. Google reprint
2. Alfred de Zayas, “Le Droit Constitutionnel et L'internationalisation des Droits de l'Homme”, Recueil des Cours de la Academie International de Droit Constitutionnel, Vol. XI, 2001. http://www.alfreddezayas.com/Lectures/tunis3_fr.shtml Alfred de Zayas, an expert on international human rights legislation, is talking here specifically about the International Covenant on Civil and Political Rights.)
3. EU Network of Independent Experts on Fundamental Rights, Opinion N° 4-2005, The right to conscientious objection and the conclusion by EU member states of concordats with the Holy See, 14 December 2005, (II.2 [page 6], "The status of international law treaties of concordats concluded between States and the Holy See"). http://ec.europa.eu/justice_home/cfr_cdf/doc/avis/2005_4_en.pdf