I'm not familiar with Caen but I do stay overnight in Reims quite often and have no difficulty finding somewhere to eat breakfast. We normally wander around the town centre and choose one of the many cafes that will be serving breakfast, you may though pay a little more if you choose to sit outside. You can of course as you say find a bakery and buy a filled baguette or croissant, many bakeries will also sell cups of coffee.
Another possibility is going to one of the large supermarkets as almost all of them will have a café attached, though I'm not sure how early they open.

Thanks Judith. We are trying to avoid going into the town centre as the museum is just off the ring road.

To be honest not been to Caen for YEARS

but overnight ferries usually put on a pretty good breakfast spread check the ferry first