This is a delicate situation. The fact that you're not 100% in love with your girlfriend in France is really debatable. You can be 100% in love with your girlfriend and still cheat on her. Been there, done that, perfectly plausible. It's our nature as males. The fact that I want to have sex with another girl whilst I'm in a LTR is either purely for having something different in my life one time two times, or there's a certain situation in our relationship that I'm not happy with. Since your girlfriend is in France, it's a situation, but not a bad one. Not a good one either, but not a bad one by far.
It's really up to you whether you go with your girlfriend or with the new HB. Neither of us can tell you who of the two you should choose and no one should. But we can tell you how to get there.
Make a list of pro's and con's. Ask yourself what will you benefit from either relationship. Does she have the qualities that you're looking for? How many of them? Which one has the most?
Then sort it out with either of them. Act with integrity.