Something else occurred to me -- would no Consul Napoleon butterfly away the Concordat of 1801? Or was reconciliation with the Papacy pretty much a done deal by this point?
The relationship between the papacy and the French government wasn't consistent during the French Revolution.
The moderate revolutionaries of 1789 were merely interested in seizing the goods of the Church to solve France's financial problems and in giving the French Church a distinct, republican organization. Striving for an independent French Church (within the Catholic Church) wasn't new; it had the main objective of Gallicanism for centuries, an ideology supported by many French Kings like Louis XIV. However, the Civil Constitution of the Clergy (a law adopted in 1790) was different in two aspect: first, the democratic spirit, since the Civil Constitution ruled that the Bishops and Priests were elected by the citizens, Catholics or not. Second, that clergymen were civil servants, paid by the state (since the clergy had been expropriated and had no own income) who had to pledge allegiance to the new order. Another interesting ruling of the time was the that clergymen were allowed to marry.
The Pope's reaction was to be expected. He refused to recognize the Civil Constitution, and recommended Louis XVI to do the same. Many clergymen equally refused to accept the new order and to swear their oath. What followed was a division between the Refractory Clergy and the Constitutional Church. Most of the juring clergymen were low clerics, and concentrated in the "revolutionary" regions (Paris, Grenoble). Around 50% of the pastors accepted the Civil Constitution. But of 136 French Bishops and Archbishops, only seven (!) joined the constitutional clergy, among them Talleyrand. The remaining positions were filled by elections, resulting in the election of men like the famous Abbé Grégoire, a radical revolutionary, democrat and abolitionist. Thus, the Civil Constitution completly divided the French clergy, which was one of the reasons why the Pope opposed the law in the first place.
The first reaction of the French legislative power was a quite tolerant one. Though the refractory priests were removed from office and replaced by elected clergymen, they had the right to rent edifices to celebrate the Holy Mass. This decree had been proposed by Talleyrand and Sieyès. But the French National Assembly was replaced by a new Legislative Assembly, once the Constitutions had been adopted in September 1791, and the new legislature was much more radical than the former one. One repressive law followed the other. Refractory clergymen were denied liberty of religion and later deprived of their citizenship. The king vetoed most of these laws, which was one of the main reasons for his impopularity. After the abolition of the French monarchy, on 26 August 1792, a decree ordered refractory priests to leave the country.
The following years saw the Reign of Terror and the repression of all Christian clergy, both constitutional and refractory. The revolutionaries even tried to replace Catholic Religion by the Cult of Reason and Robespierre's Cult of the Supreme Being. Only after Robepierre's overthrow on 9 Thermidor, the Freedom of Religion was restored. For reasons of austerity, the National Convention abolished the clergy's stipend on 2 Sanculottide of the Year II (18 September 1794). This decree is remembered as the first separation of Church and State in France. In the following months, the Convention confirmed the religious freedom and the churches were finally reopened.
The Directorate saw the zenith of the Constitutional Church. Even though France was a laicist country, the clergy was allowed to organize himself and to practice Catholic religion.* The animating spirit of this revival was obviously Grégoire, who worked towards a truy independent and gallican Church. A first national council was assembled in 1797, which confirmed the Civl Constitution. At the same time, the Directorate pressured the Pope to finally accept the Civil Constitution and to end schism afflicting France. The Pope didn't accept. A second national council was held in Paris in 1801, but Napoléon prevented it to take any important decisions, and concluded a Concordat with the Pope. The elected bishops were forced to resign, and the old schism was replaced by a new one: the Petite Église opposed both to the Civil Constitution and the Concordat.
So what will happen if instead of Napoléon, Sieyès and his followers took power in France? The government needs to heal the religious division afflicting France, and therefor a reconciliation with the Pope is essential. But it might be a more democratic reonciliation. The Pope accepts the election of priests and bishops, but clergymen have to be endorsed by the Pope. Also, refractory clergymen are allowed to return and reintegrate the French clergy. This might work, especially if you take into account that on Christmas 1797, the bishop of Imola (who became Pope Pius VII in 1800) gave a homily asserting that democracy and Catholic faith aren't incompatible, but that every state needs religion.
*At the same time, the Directorate promoted Theophilanthropy to reduce Catholic influence; but this artificial religion was later banned by Napoléon.