Hmm. It's been quite a while since I read it; I think much of the material set in the era prior to Kirk's would have to go, but not all of it. Some of that 'history' could have been related verbally in a conference or as part of a holodeck experience in the TNG era, bringing the audience up to speed on the salient points. As the 'first' TNG movie, this would have supplanted Generations and taken place some time after the events of 'All Good Things', when Picard was forced by Q to revisit the horrors of the post-apocalyptic court of an earlier age. Perhaps as a way of exploring that era with his friends, we could get some of the background info necessary to the remainder of the plotline.
Another problem is that much of this story doesn't make sense to audiences not familiar with the TOS episode introducing Zephram Cochrane and Nancy Hereford. At some point that story needs to be rehashed too so people are up to speed on what's going on. (Perhaps when an angry starfleet contacts Kirk about Hereford, who isn't quite dead as the log reflects...)
The indispensable parts of the story involve the tie-ins between the two eras- the pursuit of Cochrane's shuttle into the black hole by the Enterprise, and the way Adrik Thorsen possesses Data in the TNG era and flies into the same black hole as well. It's behind the event horizon (which a warp driven ship can escape, given enough power) that the two crews intersect and interact, and solve the problem of the prisoner's paradox or whatever is was called. Both ships eventually escape back to their respective eras, and then there is a return by both to Christopher's Landing on Earth where, in the TNG era, Picard reads the letter written to him by Kirk in the 23rd (without knowing who he's writing to, other than that it is the captain of a future Enterprise).
It would take a careful treatment to turn this novel into a filmable movie script, but the Reeves-Stevens wrote for S4 of Enterprise and if it was my movie to make I'd hire them to adapt their own work. It would definitely be a movie for Trek fans more than general audiences, and would require probably at least a 2.5 hour run time to do right. That aside, I still maintain that this story would have been a far better 'bridge' movie between the two eras than Generations was. Just MHO.
For anyone who's been interested in this thread but hasn't read the book- I can't recommend it highly enough. It's basically part and parcel of my 'head canon' since I consider the 21st Century Earth in First Contact as a splinter timeline that led to the events seen in Enterprise. First Contact contradicts a great deal of the material in Federation; if they'd adapted the novel as a movie rather than making Generations, First Contact would have been a totally different product.
Just because of cost, I would imagine either the majority of either the TOS or TNG stories would have to go.