Eurofed
Banned
Not in the 19th century it wouldn't; the French never considered it IOTL and were rather touchy about the "national territory" - neither royal nor republican juridical tradition considered it possible for the french head of state to alienate land short of a defeat at war. Andorra fulfilled all the problems and on top of it was, with Liechtenstein, one of the OTL proposals before the italian government voted the Law of Guarantees.
For Papal Avignon, Bourbon France might be willing to make a special exception, especially if the land ceded is limited. As it has been remarked, it may be at little as a few city blocks.
As for Boulangism, for all its "populist appeal" it never managed to get more than 10% of the popular vote: a Boulangist coup would have ended messily and with Boulanger's fall: the man was no Franco.
The Royalists had a majority in the 1871 National Assembly. If the Pope persuades Henry to accept the tricolor as a compromise of convenience (and he was one of the few men in the world Henry whose authority Henry would heed) "to make France the sword and shield of the True Church", he
would get the throne. Boulanger is just an example of how a late 19th century far-right Frewnch regime might expand its consensus base by marrying reactionary Catholicism with proto-fascist jingoism and militarism.
I won't say that Andorra would not be a decent alternative. It would be. But in comparison to Avignon (or Santiago de Compostela), it would lack prestige and tradition, and hence be a second-rate option for the Papacy.
The Balearics and Corsica would be even poorer choices, no prestige, the problem of alienating national territory, and Corsica was kinda unruly and too close to Italy.