I wouldn't start before halfway April. Burgundy tends to a continental climate, I went there by car in late march once, and winter was still full on. 6 Degrees Celsius below zero, a week later Dijon exploded into spring, sunny and pleasantly hot. That was a great experience, lovely city, and winter was late so everybody was getting impatient, and in turned in one day. Everybody went out in their loveliest clothes to celebrate spring in every way, just walking the streets has never been as sensual since. But I was glad I was not on a bike the week before.

And you would cross the Chablis, which is notoriously wet and grey. By French standards, so it's not that bad, but also much better in spring weather than in winter weather. Around june it can get very hot in Burgundy, so I'd try to finish before the end of may.