Actually, I don’t think it was that cynical (for one thing, the French had been heavily, if not officially, on the side of the Protestants for a long time). The Founders realized that a state church wasn’t a good idea and even though the Anglicans didn’t like the Congregationalists and vice versa, and nobody liked the Catholics, they understood that the Judeo Christian nucleus had to be the foundation of this new country.
The French (cynical opportunists as always) were not really on the side of the Protestants so much as they were opposed to the Catholic Hapsburgs of Spain and Austria. France brutally suppressed the Huguenots, either killing them or driving them from the country, much to the benefit of the lands to which they fled, including England, Prussia, South Africa, the United States, etc.