Is there a name of a company or driver who we could contact?
You could try taxi operators in Honfleur but don't expect them to be able to speak English nor to have anything more than a very sketchy knowledge of D-Day and the beaches. Honfleur may be in Normandy (a high region) but it is well out of area for the "beaches". There are knowledgable guides based in the "beaches" area itself but I doubt whether any of them would want to do the double run to Honfleur, and if they were, you probably wouldn't be able to afford their price.
When you googled "private driver honfleur" what did you think of those results?
I would try American Express Travel services or Andrew Harper and have them recommend and set up the service for you. We are going to try that. Also a big limousine company in the US that also works oversees can set up things like that.