I have nothing but respect for Bakula and the rest of the ENT cast, but I just don't think this premise has the legs to work, especially twenty years later.
Instead, I think the focus should be on the very "first" Federation starship, i.e., the first starship to be designed, build, and crewed by inhabitants of the founding worlds of the UFP. I'm sure respective fleets were grandfather in and referred to as "Federation starships," but this ship and her crew represent the first joint venture of the newly-formed Federation.
Since this ship would have a great deal of meaning for all involved, a nice reference to Zephram Cochrane and the end of the Earth-Romulan War would be to name the ship "Phoenix." Human captain, Andorian security officer, Tellarite doctor, and toss in a Vulcan engineer who is a technical advisor.
Consider the significance of such a show: different people from different worlds and backgrounds and cultures, working together for the first time on a long-range deep space exploration mission. There's a ton of relevance to our world now and loads of storytelling potential. Archer could be a recurring character along with other former Enterprise crew members.