I have read that most restaurants, markets and sites in Avignon are closed in November. We are planning a first time trip to Europe starting in Italy the end of October, spending a week between Rome and Siena. Then a second week in France between Lyon and Avignon. But perhaps we should reconsider if most things shut down at that time of year. Recommendations?
It's certainly not the liveliest time of year in Provence. A lot closes on November 2 until April. It's not clear what you mean by "between Lyon and Avignon." Do you mean that you'll split your time or that you'll be traveling from Avignon to Lyon. There's enough in Avignon and surroundings to occupy a few days in November. Lyon is a major city.
We are considering splitting the week, maybe 2-3 days in Avignon and 3-4 days in Lyon. But perhaps rent a car in Lyon and make a day trip to Avignon and a day trip to Dijon for their food festival. Would that be reasonable or too much to pack into 2 one day trips?
I would not drive from Lyon to either Dijon or Avignon: the train is faster!
Dijon is an OK day-trip from Lyon, however, I am not sure that Avignon works, because to me the highlight of Avignon is not Avignon itself, but the region it is in (including Arles!). I would stay a few days in Avignon, even in November. Or in Nîmes, which is less touristy and thus less seasonal.