Normandy has a reputation : it rains a lot. Well, this old movie "The Umbrellas of Cherbourg" certainly didn't help! Does it rain this much here? If we take Caen for instance, as it's located somewhat in the middle of Normandy, it will give you an idea. Average temperature in the winter 9°C - lowest around 3°C, and average in the summer is 24°C - lowest around 12, which means our highest in the winter will be our lowest in the summer, give or take a few degrees. Not too bad. But there's the wind to take into account, and that can make a huge difference. Average is around 20 km/h wind all year round, with storms sometimes pushing up to 90 km/h, that remains occasional. Not "rare", but it happens. 40 to 60 km/h winds are somewhat frequent on the coast.
Now the rain... well! December gets the most with 75 mm, November comes close behind it. Rain can happen any day at any time as we are on a 50 mm per month average most of the year. In percentage, it rains 40 to 55 % of the time (as in days per month). As a result, always green here in Normandy, the countryside is lush and gorgeous.
The sun comes out though, we have good days, especially in July, August and September. April to October is overall reasonably pleasant to very nice. Does that mean you should avoid coming between November and April? Not at all, because it may not be bad, especially if you layer, because in any case, you'd better layer, and you know what's fantastic about the winter months? The lack of crowds, having the sites to yourselves, enjoying a different pace. I love winters, they're not cold, not really, it rarely snows, especially on the coast. You feel "alive" and a little wind and rain are nothing with a good pair of Wellies and a nice cozy jacket. At the end of the day a shot of Calvados will warm you up from the inside.
So unless you come to Normandy just to go to the beach sunbathe and swim, anytime is a good time! For historical/cultural visits, avoid July and August if you can because that's when it turns into the French Riviera of the North.