Club opponents frequently play the French Defence again me, and I have trouble countering it with the Advance variation, since Black gets active pieces. Is there another good variation that avoids the Winawer, while giving White less problems?
Your best bet is to play the Exchange Variation with 3. ed.
[fen ""] 1. e4 e6 2. d4 d5 3. exd5 exd5
Yes, white's advantage after this is very small but you will get a more open game which is probably not what your opponent was hoping for. It has a bit of a dull, boring reputation because one line is symmetrical but there is lots of scope for both players to play more adventurously by breaking the symmetry. The tactics just take a bit longer to build.
Three most common replies to the French are
3.e5, in your question you are ruling out
3.Nd2, the Tarrasch, seems like a natural suggestion, and it is less sharp than Winawer and if closing of the center happens it is on better terms for white than in Advance variation, so it might be worth a look. But if you want to avoid French structures in general, then by all means play the exchange variation that Brian Towers has suggested.