Napoleon's concordat: Introduction and summary
The French were to be given just the right dose of Catholicism: enough to “oblige the faithful to pray for the Republic”, but not so much that Protestants were once more driven to rebel. Napoleon's method of doing this was twofold: a Concordat, signed by the pope, and his own unilateral Organic Articles which effectively amended it.
Napoleon viewed religion in general, and the concordat in particular, as stabilizing measures: “I don’t see [in religion] the mystery of the incarnation, rather the mystery of the social order; religion relegates the idea of equality to heaven, which prevents the rich from being massacred by the poor.”  He claimed that the concordat had “put a stop to disorders, obliged the faithful to pray for the Republic … and broken the last thread by which the old dynasty maintained communication with the country." 
Napoleon remained wary of the church which had supported the Bourbon dynasty. He unilaterally attached to the Concordat 77 additional “Organic Articles” that partly nullified its provisions. Pope Pius VII protested, but in vain.
Also displeasing to the Vatican which exerted pressure during the negotiations , the French Catholic Consuls refused to use this concordat to impose their personal beliefs on the whole nation. This contrasts with Germany where the ruler, whether Catholic or Protestant, claimed the right to dictate the religion of his subjects. (Cuius regio, eius religio)
In France, however, the genie was out of the bottle. The secular ideal of individual freedom of religion, born in the French Revolution, could not be ignored. The 1789 “Declaration of the Rights of Man” guarantees freedom of religion "provided that [...the] manifestation [...of religious opinions] does not trouble the public order established by the law". This is exactly how Catholic worship is treated in the first article of the concordat.
Napoleon, of course, had practical reasons for wanting to maintain individual freedom of religion. A century earlier the Catholic Church’s attempt to exterminate the French Protestants had made them rebel. History had shown that, in the long run, religious repression was not in the interest of “the social order”.
This concordat was modelled as closely as circumstances permitted on its predecessor. “Save in the provisions relating to ecclesiastical benefices, all the property of which had been confiscated, it reproduced the concordat of 1516. The pope condoned those who had acquired church property; and by way of compensation the government engaged to give the bishops and curés suitable salaries.” 
The concordat lasted just over a century. In 1905 it was cancelled by the French National Assembly when it passed a law to separate church and state. The law famously states, "The Republic neither recognises, nor provides salaries for, nor subsidises any religion".  This law is the backbone of French laïcité or secularism, “the absence of religious interference in government affairs, and vice-versa”. 
Summary of the Concordat (full text)
The preamble acknowledged Catholicism as ‘the religion of the great majority of the French people’, a wording which did not altogether please the Curia which had initially demanded that Catholicism should be the ‘dominant’ faith. Article 1 permitted the free and open practice of Catholicism, albeit in a way that did not disturb public order; Articles 2 and 3 foresaw the reorganisation of dioceses after consultation between Paris and Rome and the consequent resignation of bishops where necessary; Articles 4 and 5 placed the nomination of prelates in the hands of the First Consul, canonical institution being subsequently conferred by the pope; Articles 6, 7 and 8 obliged bishops to swear an oath of fidelity to the government and to recite prayers for the salvation of the consuls and the republic; Articles 9 to 12 dealt with the internal organisation of the Church; Article 13 asserted the inviolability of the lands seized from the Church during the Revolution; Article 14 made a vague promise of a ‘suitable salary’ to clerics to be paid by the state, while Article 15 allowed endowments to the Church; and the catch-all Article 16 conferred upon the First Consul the same rights as had been enjoyed by the Ancien Régime monarchy over the Church, without specifying what these entailed. A final article accepted that, in the event of a non-Catholic assuming the position of first Consul, the concordat would be renegotiated. 
Summary of the Organic Articles (full text)
Ostensibly these dealt with the policing arrangements referred to in Article 1, but in practice they went much further. Government approbation was required before papal pronunciations could be published, councils convoked, new parishes established and chapels set up. A uniform catechism was introduced, church weddings could not precede the civil ceremony, cathedral chapters were reduced to merely ceremonial function and the powers of papal delegates were severely circumscribed. Any breach of the articles was treated as a criminal offence and was referred to the Council of State, the keystone of Napoleonic government. Additionally, clerical salaries were specified, a mere 15,000 francs per annum for an archbishop of whom there were to be ten; 10,000 francs for each bishop who numbered sixty in total; and 1,000 to 1,500 francs for the 3,000 or so parish priests. Although it was not specifically referred to in the Organic Articles, the creation of a Ministry of Cults in 1801 reinforced a drive towards government oversight of ecclesiastical matters. 
1. «Quant à moi, je n’y vois pas le mystère de l’incarnation, mais le mystère de l’ordre social ; la religion rattache au ciel une idée d’égalité qui empêche le riche d’être massacré par le pauvre.» Napleon I, 4 March 1806, quoted in Joseph Pelet de la Lozère. Online: Hippolyte Taine, Les origines de la France contemporaine, V, 479-480.
2. “Napoleon I (Bonapart)”, Catholic Encyclopedia, volume 10, 1911.
3. “The French Concordat of 1801”, Catholic Encyclopedia, volume 4, 1908.
4. “Concordat”, Encyclopedia Britannica, 1911
5. “1905 French law on the separation of Church and State”, Wikipedia.
6. “Laïcité”, Wikipedia.
7. Frank Tallett and Nicholas Atkin, Priests, Prelates and People: A History of European Catholicism Since 1750 (Oxford University Press, 2003), p. 73.
La négociation du Concordat (1800-1802)
8. Frank Tallett and Nicholas Atkin, Priests, Prelates and People: A History of European Catholicism Since 1750 (Oxford University Press, 2003), p. 73.