We like Bistro Zinc on N. State Street. Staying "downtown"is a rather broad description. In the Loop or River North, Streeterville, or along Michigan Ave? Regardless, you'll enjoy Bistro Zinc.

bistronomic is a nice place.
http://bistronomic.net/hostalt/
Especially if you can sit behind the bar for a bit more quiet.

Not downtown, but Bistro Campagna in Lincoln Square is very nice.
http://www.bistrocampagne.com/

How about Cyrano's? We had a great time there for Bastille Day.

We like Bistrot Margot, in Old Town on Wells (http://www.bistrotmargot.com/). Not exactly "downtown" but it's good. And if you're visiting Second City or the Chicago History Museum, it's right there.

Those within a $10 cab ride of downtown are

Bistrot Zinc, Bistrot Margot or Cyrano noted above

Also La Sardine (West Loop or River West they might call it)

or Kiki's Bistro (just north of Downtown and right on the Brown line of L, exit at Chicago stop if your hotel is near that line)

Margot, Zinc and Cyrano's are all nice. Kiki's is very good. Bistronomic is very nice but a little more expensive. Mon Ami Gabi by the zoo is more of a Brassierie but is also good.

http://chicagovisitor.net/French.html

Kiki's Bistro is a favorite of ours but you need to take a taxi. One time we were there, Julia Child was dining there too, a great testimony.