There is also a chance of them inheriting the throne of England after Elizabeth dies, so they get both thrones of England and France but they will have problems with the protestants.
Only if it's a boy. Also, the problems happened in reverse with catholics IOTL anyway.
I'm not sure, however, that the English would take turning into a province (actually 4-8, see below) of France without a fight, but this situation would lead to a few options
- France becomes even more of a hegemon, with England and Ireland grafted to it
- France eventually loses the islands to rebellions
- Something in between
- France retains the islands but doesn't follow the same centralizing impulse as OTL, thus avoiding "proto-nationalist" rebellions, but becoming a bit of a mess - we'll call it Francia-Englary
(this is not quite accurate, of course, but you see what I mean). Admittedly pre-revolutionary France was already a mess.
This also somewhat lessens the impulse for colonization; that said, it's possible that this leads to a french eastern seaboard anyway, just "french" instead of french in my third option, as the provinces most likely to colonize are, well, only two speak french.
If England-Ireland ends up integrated to the french legal system (and trust me, if it doesn't revolt away, it will), I could see a minimum of four provinces - Ireland, England, Wales & Marches and "Northumbria" based on the chanceries. Given how some provinces formed, I could actually see the following added to that list: Lancaster (Lancashire + duchy lands), Cornwall (Cornwall + duchy lands; IIRC this represents enough of Devon that most of the county would be in it) and Chester. A situation somewhere between Guyenne and the Loire (one was a mashup of multiple royal and feudal estates, the other was split into multiple provinces)
I still don't think it holding together is very likely. If it does, though, you end up with a much weaker social position of english, especially when considering the state of english finances at the time and that it's going to lose direct control of its dependent countries.