Great translation! I'm actually impressed how well you hit the nail on the head with some of the lyrics!
I noticed a couple of things though.
1. "J'airais aimé" is le future antérieure, so in english it would be "I would have liked to tell you words you've never heard". Also I'd favour "tell" over "say" in this one. "Telling" implies it's aimed at someone (i.e. the person he's singing about), whereas "saying" is less specific and more directionless.
2. "because "because in my eyes 'I love you' has become far too common". I'd add the "far" in there to more precisely convey the "bien trop".
3. I'd say "I will vow to pleasure you" rather than "commit". I tried to think of a way of saying "à ta cause" but it doesn't really work in english unfortunately..
4. I'd say "if it could please you" rather than "can". But I'm not sure it makes much difference really, I think either are perfectly good.
5. "just let me prove" rather than "only". And to translate "que ce n'est pas du vent", I have absolutely no idea haha, I don't know of an equivalent expression in english... I mean "hearsay" is equivalent but doesn't really fit the sentiment of the lyric. But with that word it would be "Just let me prove to you that it's not hearsay".
6. "just to let me love you" rather than "only"
7. "Donc je ne compte pas la laisser tomber" would be "so I'm not going to let her down"
8. "si tu nous laissé...(rien qu'une fois)" would be "if you gave us...(just one time)". Which yeah actually, I'd say "just one time" for "rien qu'une fois". "just once" sounds like an event that happened only once. Really I would change the translation altogether to "just one chance" as that makes more sense, but i'm always reluctant to *change* song lyrics in translation..
9. "jusqu'au bout des doigts" is a weird one, because it's not literal. the expression is equivalent to "by heart" so "I will learn each part of your body by heart" but again... that's completely changing the lyric...
10. "You wont have to push me to hear sweet words straight from my mouth" I'd word it like that
11. I like your choice of the word "nifty" haha, "neat" can also work
12. "Small stuttered movements, suddenly I stop" is how I'd word that one
13. "The floor is yours but you remain silent" I think works good
14. "because I'm going to give you so so much"
15. "that your body will completely give in"
16. "I will reveal your inner talents that until now you weren't aware of"
17. lastly there's the "elle est belle, elle est belle oui elle est belle et élégante" bit which I'd translate as "she's pretty, she's pretty, yes she's pretty and elegant"

Lol honestly when I scrolled down to comment I did not expect to leave something so in-depth haha
well I hope you find it useful anyway!
But good job with the translation, there's a couple of lines that I like a lot and better found than 99% of lyric translations I've read online!