I wouldn't dismiss 3.e5 as a serious try.

Indeed Tzermiadianos's repertoire book is probably my favourite White repertoire book against the French (though to be fair I don't have that many). Even a lazy option like 3.exd5 exd5 4.c4 (opening the position against a player wanting a closed position) has worked well for players like Miezis, but I'd suggest learning the Advance French. There's Sveshnikov's two books on the opening for White, and while it doesn't offer an advantage, it's not at all clear that 3.Nd2/3.Nc3 does either, and once you learn the theory and understand the key middlegame ideas (starting with when to time b4-b5 and g4 to kick knights away from c6 and f5) you'll have a dangerous system for life. The equal positions are generally very complex and it's extremely tough for Black to steer the game towards a dull, lifeless position. Other than Sveshnikov, Grischuk is the big Advance expert for White. 

If you still have problems against the French as White after following our suggestions, perhaps this will be your calling to start a very successful career with the French as Black! 

I've had great success (+4=1-1, 2194 performance compared to my usual 2003) with a repertoire based on Tzermiadianos' How to Beat the French Defense. It's based on the Tarrasch and there are lots of almost-main-lines (i.e., he deviates but on move 9 rather than 4). Honestly 1...e6 is the move I like most to see.

I need some serious help sorting out my struggles from the White side of the French.

Some background for understanding: I am ~2100 FIDE, getting back into competitive play after a few years hiatus. I am looking at future long-term competitiveness, and so am looking for an opening I can feasibly stick with for the foreseeable future. Main goal is to be competitive at 2200-2400 level. I have no qualms with deep study and learning theory if necessary (and am doing so in several other areas of my repertoire).

I was a 1.e4 player for my first 6 years of play, from beginner up to 1800. In 2005 I switched to a Catalan based repertoire. I scored well with that, but never felt entirely at home. I've decided to move back to 1.e4. The French is my primary struggle to come to grips with, as the literature is pretty saturated on the Black side of things currently.

I've always performed best with side variations of Main Lines, where I can throw the game into slightly original territory, develop some ideas of my own and battle it out from a solid foundation. Slight advantage positions where I can neutralize counterplay and let my opponent stew and self-destruct have always been huge point-scorers for me. In my early career I was a Tarrasch devotee. These days I can't find a line that I feel confident in, I feel like Black is in a pretty happy place in terms of theory there. I've toyed with 3.Nc3 as well as the Advance in some online exploration, but have yet to find any positions in them which feel comfortable. They don't seem to click for me intuitively, and I again feel like Black is satisfied with theory as covered in recent literature and advocacy for Black's cause.

So in frustration I turn to you. No other openings feels as threatening to my 1.e4 prospects as the French does right now.