I think if First Contact were made today, it would be about two and a half hours long, and the A-plot (the Borg on the -E) would go pretty much as we saw it while the B-plot (Zefram Cochrane) would have a secondary antagonist, like Cochrane needs to launch the Phoenix at a certain time not only so the Vulcans detect the warp signature but also because some faction in the 21st-century conflict is bearing down.
Would that be an improvement to the film? Maybe. Maybe not. Perhaps there's a better way.
To me, the Cochrane plot in the film feels very tangential. Partly, it's the tone of the thing -- you have high stakes in one plot line, and you have Troi getting drunk in the other. And the connection between the two, even though Picard states it baldly about ten minutes into the film -- "The Borg are trying stop first contact" -- feels tenuous. The threat of the Borg to first contact becomes theoretical rather than actual.
I think it might have been better if the Borg put actual drones on the ground when they arrived in 2063. First, they attack Montana from orbit, when the Enterprise shows up a squad of drones beams to the surface before the sphere is destroyed, and then Picard had one fight on his hands on the ship while Riker has another on his hands on the surface -- repairing the Phoenix and stopping the Borg squad from disrupting the launch.
That kind of change would better unify the two halves.