Not neutral. Loyal to those that have built up loyalty there. Sure, if they can stay with French control, they will. If France has an "administrative" influence (ie. a city) within the area the tiles will remain French. But if you remove the French "administrative" influence on the tiles by conquering all French cities within range, then it reverts to the second most influencial "administration". In this case, it's the Germans, as their cultural influence on those tiles is much stronger than yours. You can still claim them, but it will either take effort culturally, or militarily.
That's far more realistic than if they were to simply go to work for you now, ignoring their German heritage and the fact that you have little or no support in the region.
You are trying to claim tiles that not only are French, but somewhat German too. They are certainly more German than they are "you". It's disputed territory among the countries involved, and a third party, taking out one side, isn't getting rid of the claim of the other side so easily. Fight them both (or all) for it, militarily or culturally. It's not just going to be handed over to you, nor should it. That would be unrealistic.
No, the lines aren't realistic. Using a tile system they just can't be, as disputed territory is very rarely box shaped. But the abstract of what is being represented actually is realistic.
Well, perhaps you can't stop it. I can. So your statement "You cannot" is wrong. "I cannot" would have been correct. Your being inept doesn't make me wrong.
What I was saying though, which you have misunderstood, is that you have military recourse to do what you say should be possible to do, militarily claim the land for yourself. You say you've militarily claimed the land? Then go enforce that claim. Go remove the German influence militarily. They are claiming that land, and have a stronger "peaceful" claim to it than you.
Otherwise, if you want to peacefully claim the land, you need to have a stronger "peaceful" claim to it than they do.