Normandy Morning tour for group of 10

That's a full van; all you need is a company that wasn't previously planning to use all of its vehicles that day and has a guide willing to work then.

I assume it's the Normandy beaches you're interested in. I'd start with Overlord Tours. They run most of their trips from Bayeux, but the company website indicates that they're willing to pick up clients in Caen for their regular full-day tours. For a private tour, I'd expect that sort of flexibility.

A half-day tour is extremely short. Six hours would be a lot better than four.

Overnight in "Normandy" -- which is a pretty big place -- at least one night so you actually have most of a day in "Normandy".