It seems like the most opportune time to accomplish this would be in 940-1, when Otto invaded France with the support of Hugh the Great and other French noblemen. The problem is that Otto was quite sane, and understood that a weakened Louis IV (who was also his brother-in-law) under East Francian tutelage was the best possible outcome. As Louis' overlord, Otto could attract the support of Hugh the Great and other counterbalances to the power of the French king; as King of Francia himself, those same powers would be working against Otto. A similar situation existed later in Burgundy, where Otto was happy to acquire the allegiance of King Conrad. Italy was only annexed because holding Italy was, practically speaking, necessary to retaining the imperial title. In all other cases - France, Burgundy, Denmark, Poland, Bohemia - Otto was quite content to assert his suzerainty without resorting to annexation.
Accomplishing this would, IMO, require either a brain transplant for Otto (and it would have to be a
worse brain, since his OTL strategy was eminently sensible) or some series of events in West Francia in which the realm falls into chaos and actually taking the crown becomes a better alternative than simply mediating among lessers.
Would Otto and successors be able to drive out or subdue the Normans of Normandy?
I can't see a particularly good reason for him to do this, at least initially; William Longsword had supported Otto against Louis IV. They might be trouble if Otto were to actually become king in France, but presumably no more trouble than any other powerful duchy. They certainly won't be "driven out" more than a generation after settling there (driven out to
where?).