The more you look at the evidence the more plausible it becomes that FC created an alternate timeline. Similar to the original but subtle differences do to pollution of the timestream by the Borg and ENT-E crew.
I just rewatched the TNG episode First Contact where Picard says the Federation's first contact with the Klingons led to decades of war. However in the ENT episode 'Broken Bow' we saw first contact with the Klingons and there was no open hostilities that caused a war. Even up to season 4 of ENT, the Klingons and Earth had a uneasy but mutual respect for one another.
What changed? Why does the history Picard state happened (First Contact 1991) contradict what was shown in ENT in 2001? The Temporal Cold War is your answer. Future Guy a being from the 28th century gave the Suliban technology and directives to help him change/rewrite history in his favor. Just like the Sphere Builders used the Xindi to change what would happen in the 26th century in their war against the Federation and the Enterprise J. Using time travel alters the past and creates alternate or parallel timelines. A new series of events that would never have occured if time travel had not been employed. Had the Suliban (who were following Future Guy's orders) never shot the Klingon Klaang down in Broken Bow, Oklahoma. First Contact between Earth and the Klingons would have been different and likely more hostile.
It's because of Future Guy, and the Sphere Builders meddling in the past that Archer and his crew became apart of events to make sure history played out like it should have unaltered. Had Future Guy the Sphere builders and the Na'kuhl never attempted to change history with time travel. We can assume the NX-01 crew would've had a very uneventful first couple of years as they explored.
With regards to the name Enterprise. It's likely named that because Deanna told Cochrane the name of their ship and Riker showed Cochrane what it looked like. Cochrane who worked on the NX project probably suggested the first warp 5 ship be called Enterprise after his experience with the ENT-E crew like T'Girl said.
With what we see before in TMP with Captain Decker showing Ilia all the ships named Enterprise but we don't see the NX-01. In STID Admiral Marcus has a model of the NX-01, but Picard has no such model on the ENT-D or E. In "Trials and Tribble-ations, the Temporal Star Fleet guys refer to Kirk's Enterprise as the "first enterprise". The Terrestial year for Trials and Tribblations is 2373, with the stardate being 4523.7. FC the movie the terrestial year is 2373 but the stardate is 50893.5. In Star Trek Nemesis we see one of the ships the ENT-E was supposed to rendezvous with is named USS Archer, after Capt Archer. I'm not saying Jonathan Archer and his crew did not exist in the original timeline. I'm saying that had the effects of the Borg, Future Guy, Na' Kuhl and the Sphere Builders not polluted the timestream by trying to rewrite it in their favor. Archer and the crew of the NX-01 probably led an uneventful tour through space. They certainly wouldn't be getting visits from Daniels in the 29th century about how important their mission was every couple of months.
The evidence is almost conclusive that ENT occurs in an altered timeline different from the original. I try to detail things out as simply as i can. When dealing with time travel and it's effects it can get very confusing. But i've given episodes and movies where things occurred and evidence can be gathered.
