First of all, of course France would react hostile to Ottoman successful attempt to take over Italy, even if we ignore the religious aspect, the fact is that taking over Italy was a pretty major French goal, they're not letting someone else take it, no matter whether they was semi-allied with the power in question earlier.
The reaction of the European powers to the Ottoman takeover depend on when it happens. If it happens in the 15th century, we just see a new Avignon exile, if it take to long to reconquer Rome the Germans may set up their own anti-Pope simply because a Pope in Avignon mean more French influence on the Church. I also think there's a good chance that Church are weaken against the states, resulting in a kind of High Anglican-style Catholic Church in Europe. If it happens in the 16th century, there's good chance that Protestantism are reabsorbed into a much more tolerant protestant light Catholic Church.
The effect of a Catholic Millet are pretty interesting, for one it likely mean that the Albanians and the Bosniaks stay Catholic (this doesn't mean some won't convert, but they will likely be a smaller number), when they have their own religious representant, even if the Ottoman Church lose Rome again this millet will likely survive, and the Ottomans will likely move the Ottoman Pope to Constantinople. The ownership of the Italian peninsula will also have other effects, for one increased income, but even if Venice aren't conquered, it will lose its position as a mercantile power earlier. Maybe Venice will be able to change with this change forced on them earlier, into a more standard European power. It do sit on some of the richest European farmland.