Much of France, especially Parisiennes, take vacation time in August, so you are likely to encounter some businesses that are closed. That shouldn't deter you however, since many of those French vacationers are visiting the same wine regions as you, so there will be lots open. I have visited both Beaune and Colmar in June, and Colmar in late August, and biking was a big part of each visit. I found the Alsace routes more interesting, in that there was more to see in the towns we stopped in, and there are more of them. However, the actual biking experience was in Burgundy was nicer- almost entirely off-road, through the vineyards on paved laneways used only by bikers and farm vehicles. The Alsace biking involved more time on public roadways and traffic. In Burgundy we biked as far as we were able in one direction, then hopped on a train back into Beaune (with our bikes), which was very convenient. I also found the Alsace to be more challenging in terms of hills, at least as you get farther away from Colmar. It's fairly flat close to town, but beyond, say, Egusheim, there is more up and down. On our second trip there, last August, we rented e-bikes, which made things much easier. And regardless of what wineries may be closed to visits, the bike trails will remain open, and the grapes will continue to ripen on the vines.
One very pleasant drive (by car, not bike) we made from Colmar took us to Staufen, Germany, on the edge of the Black Forest. It's a pretty little town, popular as a base for walkers. Another interesting spot was the Haut-Koenigsbourg Castle, about a half hour drive north of Colmar.