Welcome to CruisersForum, AdaLouise.
As goboatingnow wrote, there are now 2 marinas
in Brest: the old one (Moulin Blanc, to the east of the merchant port) and the new one (Marina du Château, very close to the naval base). In fact, to enter Marina du Château, you have to go through the naval base entrance and go north (DON'T turn to port!). Both marinas
are operated by the same company.
Marina du Château: +33 2 98 33 12 50 - email@example.com
Marina du Moulin Blanc: +33 2 98 02 20 02 - firstname.lastname@example.org
The company website isn't really running presently, so you will have to write to get more details.
When I stop in Brest in summer, I prefer going in Marina du Château because it's much closer to the city center. From there, you can take a streetcar or city buses. In Moulin Blanc, you have to walk a lot or take a bus to go anywhere: the nearest food
shop (a supermarket) is 1km away.
For wintering, I would prefer Brest over Morlaix, because it's a bigger town, there is a busy airport
(flights to London, Birmingham and Southampton) and I suspect there are more resources for taking care of a yacht (boatyards, yachtchandlers, etc.). Yes, I'm partial: I was born in Brest
Or you could come to South Brittany, where the climate is milder...