Shoud I stay one night in Rims and 3 in Beaune?
According to viamichelin.com it's a 4-hour drive from Bruge,Belgium to Reims and another 4 hours to Beaune. That's on major roads. If you want to stop along the way at a village or sight, the driving time will be longer. You could probably manage to do 1 or 2 champagne tours and tastings in the afternoon of your arrival in Reims, if you leave Bruge early and don't stop, and fit in a couple of the other sights there. Then leave in the morning (maybe a little more sightseeing before you go). Or get an early start and have time to stop for a village or two, arriving in Beaune late in the day.
Since you have a car, why not stay in a village B&B in Burgundy. That will save you both money and time driving in/out of Beaune. Avallon, Vezelay . . . . just a couple of ideas. After your 2-3 nights there, you could spend 1/2 day in Beaune, then drive to Cluny (or Annecy) for a night, then on to Chamonix.
Edit: Spending a second night in Reims gives you the time for more champagne tours and tastings, including a visit to Epernay. Mostly it depends on whether you want to give up a day of Burgundian villages for a day of bubbly.