Do we know that the Franklin was a one-off prototype? I don't remember any one saying that in the movie.
You're right, we don't. But we don't know a lot about the Franklin other than she's older than the NX-01, yet has a higher registry, and she was the first ship to make Warp 4.
She
could represent a class of limited-production run ships to fill out a small human fleet before NX-01. We have seen a few other earth ships that were not the Enterprise (The Intrepid), and Franklin may have been the preceding class. Then when all of Earth's fleet ships were imported into Starfleet all of them got re-designated. Her high number might
not be because she is newer, but because she entered the fleet
later. All the NX prototypes, the Intrepids and others, were inducted into Starfleet before the older Franklins were brought out of storage to fill the fleet, and got a higher number.
Later when the Federation started building unified starships, they stared getting NCCs as their prefix. NX may have remained as "earth-type" until being reclassified for use as experimental ships. Or, we can infer NX means any human-origin ship, suggesting Excelsior was designed by humans until being inducted into starfleet. We don't know, because I think Starfleet hull designation codes are determined by inference, rather than a detailed system.
If there was a Franklin pre-production class, then the unlucky veterans got the older Franklin-class ships to fly, and it's only coincidence herself that the prototype and class ship ended up being lost on Edison's command.
There is something else of interest to note about the Franklin: She has a bridge window to space. If she's from the Pre-nero days but still in the same universe as ENT, it's the first ship from old canon we've seen with a window viewport like this (not counting the Enterprise from the pilot episode, of course). Even if you don't like it I can believe the Earthfleet experimented with this, coming off of the Pheonix, before feeling confident enough to enclose the bridge and use a viewing screen in the NX-01 prototype.