> What is bothering me is the use of "tu" instead of "vous" :
> 
> I don't really know how to react to this. Why being so informal ? Am I
> over thinking this or does it scratch you too ?

You are overthinking this by a huge margin.

But if it bothers you this much, instead of pondering why someone would use "tu" instead of "vous", just ignore this recruiter and only respond to recruiters who are much more formal.

It's a waste of time trying to play "let's guess what the recruiter was thinking" here. Just decide how much you want to let this bother you, then act accordingly.

I studied French for many years. I understand "tu". Again, there's no need for a conundrum here. If you don't like whatever a recruiter writes in an email, just move on. I would do the same if the email contained a ton of typos or grammar mistakes, or if the recruiter didn't understand my profession. It's simply not that difficult of a choice.