If you want to be the friend of France forever, build a bench of vassals between you and France. At least, that was my way to save the alliance in 1.7. I don't know exactly why, but it helped.
Not sure if it's a new 1.8/AoW mechanic, but countries can desire the provinces of your vassals too and they will hate you for that (and probably the vassal too, but that's the unimportant part). At least that's what I recall, might have been dreaming about that (not really), but I had that in my game.
I'll give you an example that describes this situation - Say we are best friends for years. One day you decide to sit on a bench. It's a nice bench. I come over and see it - and want to sit on it too. There is plenty place for both of us to share - for now. But instead of sitting down next to you, I slug you in the face and tell you to move out - or I'll do worse. Five minutes later, I remember I need to go shopping, so I don't want to sit on the bench anymore and suddenly act all friendly again, completely forgetting the fact I just punched you in the face.
Not 100% parallel, but close enough.
The example works about the sudden changes that happen from friendly to hostile, from hostile to friendly, but you're forgetting that just because there's other room it doesn't mean it make no sense for you to want the entire bench. Maybe France doesn't want a country getting too strong on its borders, so instead of starting some sort of a cold war by taking more territory than its neighbor, it instead does two-in-one - both takes provinces and ensures the enemy has less provinces.
As a player, I do that. Ex. when Burgundian Inheritance triggered in my playthrough as France - I did initially keep my alliance with Austria, but eventually, when I had become strong enough (as in - noticeably stronger than Austria & all her allies combined), I betrayed them. It's only logical an AI would do similar - it's smart. But yes, the problem is how the AI changes its attitude from one day to another so suddenly and then, disregarding the backstab it did, it simply goes back to friendly again at some point, pretending nothing happened.
It's because diplomacy is all based on numbers and modifiers, a random mission giving claim on an ally is such a huge modifier that it outweighs any other positive ones and destroys the friendship. I don't think that will change, but I think they could somehow make those modifiers creep in slowly, change over time, not so suddenly, and have the AI realize consequences of its actions. But in all honesty, probably will stay this way - maybe in future PI games the diplomacy AI will be based on some more sophisticated and advanced systems, but, for now, numbers is best we can get.