Pay attention because there will be a quiz on this after. This is not your mother's starship Enterprise. It is not the Entterprise at all. Why? FX6-1995-A is not a valid Federation registry number. Here are the ten ships recognized in official Star Trek canon:
While the starship model in Vulcan, Alberta that tourists love to photograph and pose with is obviously a (ahem) modified Constitution II Class (refit of the original Constitution), the registry number is a bit more, er, local. FX6 is the Vulcan airport code. 1995 is the year the model was erected. The A stands for this being the first one erected. Model B will only happen after Model A falls on a tourist.
So whatever this ship is, it is not the Enterprise. At least not in the regular universe. Mirror universe? Maybe, but unlikely. Now, please close your textbooks and put them away as the quiz is starting.