White fights for equality in French classical? Normally, using engines for any given opening I can find ways for White to maintain a slight edge into the middle game. By a "slight edge" I mean an evaluation of around +0.20

The exception to this is the Classical French (and Steinitz), where it seems like every line Black has at least equality and most lines lead to an edge for Black!

For example, in his book on the French, Psakhis says that after 1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. Bg5 Be7 5. e5 Nfd7 6. h4 0-0?! is dubious for Black after 7. Bd3. However, the engine shows that not only is not dubious for Black, but Black has the advantage after 7...c5!

This is just one example. No matter what line I try, Black always seems to get at least equality.

Even more scary is that not only is Black always getting equality, but White seems to have a lot more ways to go wrong than Black in many of the lines.

Is there any line in the Classical where White can retain a pull?

I am using Komodo 10 as my engine.
An evaluation of +0.2 is just noise and nothing like a "slight edge". Another engine might very well give you -0.2 or so. I would not be overly concerned by such evaluation. 

When analyzing opening lines, much more important is the character of the position: whether you like it, whether it  gives you winning or drawing chances (depending on requirement), whether it is easy to play for you (and difficult for your opponent), etc. All of these are difficult to assess automatically with a computer and require you to look at it. That's why GM spend so much time on openings and don't just have their computers running looking for the line with the highest evaluation.