At first I misunderstood the Picard Maneuver, since I was busy tending the popcorn instead of paying attention to the show. I like my version better:
One fires the phasers while entering warp. As the phaser beam leaves the warp field, it drops to sub-light... and is then immediately overtaken by the field and re-accelerated back to warp speeds. When the ship drops to sub-light, the phaser beam has been compressed to many times its original density, making it much more powerful. Where did this energy come from? The main engines, through the warp field. Very inefficient, and it would probably burn something out... but this is why it would be a specialized maneuver, not the standard way of attacking someone.
Alternately, one fires the phasers from a great distance, then warps in at a slight angle and fires again so that the two beams arrive at the same place at the same time. Time on impact, with the same gun.
But neither of these is the 'actual' Picard maneuver.
By the way, the 'actual' Picard maneuver relies on the victim (advanced FTL sensors or not) failing to realize that he should pay attention to the big image of the nearby ship rather than the little tiny image of the faraway ship. This might fool someone the first time, yes. But it obviates the need for Data's scientific excursions. They completely ignored the effects of perspective. Wow.