Coins are easy to accumulate. I had to do that in Nice a couple months ago, since all the machines for train tickets only took coins, even for tickets around €10. I just paid for everything with notes. I got 50's from the ATMs, paid for small things with them whenever it seemed possible to get smaller notes. You'll usually pay tolls fairly often, so they'll be small amounts. Feed the machine a €10 or €20 note and you'll get all your change in coins.
I spent over a week driving in Alsace and Burgundy and only took the autoroute (toll road) when I was in a hurry. The lesser roads are much more scenic and go through all the charming villages that you want to visit. You'll also need coins for parking machines in many towns and villages. The ones I encountered most, and often in parking lots, one had to park, walk to the machine and buy a ticket for a period of time, then display it inside on the dashboard.
Warnings - the autoroutes are monitored by sensors and you can get dinged with speeding tickets very easily. Get instructions on the cruise control when you pick up the car. It's all to easy to be distracted by everything else and accidentally go over the limit. Speed limits are always posted on the autoroutes, not always on side roads. Unless posted otherwise, they are determined by law by type of road. You are expected to know them (and all the other rules, like no passing on the right). I'm sure there's somewhere on the internet you can find a summary. My trip was several years ago, I know I read up on them but forget where. Warning signs are only in French - learn the vocabulary to make it easier. I think many roads other than the autoroute are also monitored for speeding. I often saw other cars going well over the limit. I made it a practice to pull over for them to pass me whenever possible, figuring they knew where the traps were, but not taking any chances myself. Alcohol limits are lower in France (0.5%, compared to 0.8% in the US).
Road maintenance and signage were very good in Alsace, not so much in Burgundy. Most of the roads were 2-lane and I didn't encounter much traffic (my trip was mid-June) but there are no shoulders, even on major roads. There are cyclists, though.
I drove a lot, only got lost a couple times trying to get to real back-roads places, and had a wonderful time. Bon Voyage!