I can't advise you specifically about Normandy, but I can share what it was like on the Riviera last year over Ascension weekend, and we might be able to extrapolate from there. First, be aware that the official Ascension holiday is Thursday the 21st, but many people will take Friday the 22nd off, thus gaining a 4-day weekend. On the Riviera, there seemed to be a lot of French people on weekend trips, as well as some foreign tourists. For the most part, tourist services were not only open, but quite busy.
Will you still be in France the following weekend? It's a holiday weekend too; Monday, 6/1 is the public holiday for Pentecost. Last year, I got caught in a huge traffic jam leaving Aix-en-Provence on the Saturday morning of that weekend.