But if the events of First Contact don't happen in this timeline then the events of Enterprise will be substantially different than they were depicted in the series. Or maybe not.
Time to take some aspirin now.
There wasn't a Tasha Yar fighting in a brutal war against the Klingons in "our" timeline. But nevertheless such a Tasha Yar appeared out of thin air in the 2340ies and had a child which was to become a commander in the Romulan fleet.
So, it's possible that in this "new" timeline an Enterprise-E appeared in the year 2063, despite the fact that such a ship won't exist in this timeline's future.
2366 - Lt. Tasha Yar travels back to 2344.
2344 - Tasha Yar helps to defend the Klingon outpost on Narendra III, which alters the timeline in such a way that a future Federation-Klingon war is erased from history. She is then captured by the Romulans and gives birth to a child. In the meantime, Tasha Yar's younger self still grows up on Turkana IV.
2364 - Tasha Yar's younger self, who has also become a security officer on the Enterprise-D in this timeline, is killed by Armus.
2368 - The crew of the Enterprise-D encounters Sela. They have no clue where a child of Tasha Yar could possibly have come from.
2373 - Enterprise-E travels back to 2063.
2063 - Enterprise-E stops a Borg invasion of Earth.
24th century? - Nero travels back to the 23rd century.
23rd century - Nero alters the timeline in such a way that (among other things) the Enterprise-E possibly never gets built.
The question which should let you really lose sleep is the following: When the Enterprise-E travelled from 2063 back the 24th century shouldn't they now end up in the new timeline's 24th century created by Nero's temporal incursion?

Or maybe not...