Really good French restaurant, not too pricey?
Mon Ami Gabi is worth looking in to. Lincoln Park neighborhood (so north of downtown) and can be done in your price range. If you are willing to venture to the West Loop, then La Sardine is an option that also can be done at your stated price point. In downtown is Henri - but that would involve going a bit over the $50 price point.
Le Bouchon and La Sardine are excellent and relatively authentic French bistros. And with entrees in the 20s, I think doable inside your price point. I think both are quite good. Here are the websites:
Mon Ami Gabi disappointed me. Part of a chain, it features steak frites with options of many cuts of beef and a variety of sauces. It is certainly reasonably priced, but struck me as way more American than French.
The other option that I love is Bistro Campagne in Lincoln Square. I have only been there once since Chef Michael Altenberg passed away last year, but the staff was committed to sustaining quality. Focus is on organic ingredients from sustainable family farms and VERY good food.