Well started the second leg trailing by a goal, having lost out in France to a solitary strike from Pascal Berenguer, who started on the bench at Fir Park.
The Steelmen started brightly and put Nancy under pressure in the opening minutes, but the French side doubled their aggregate advantage with 18 minutes on the clock.
Benjamin Gavanon's 20-yard free-kick was parried by home keeper Graeme Smith and the loose ball fell to Marc-Antoine Fortune, who rifled it home into an unguarded net from five yards out.
Four minutes after their first goal, Nancy struck again to all but make the tie safe as they took a three-goal aggregate lead.
Gavanon curled in a free-kick from the left corner of the penalty area and it eluded a clutch of players in the box, before dropping into the far corner of the net, with Smith rooted to the spot.
Well pushed to try and find a way back into the tie, but the visitors' defence held firm up until the interval.
Monsef Zerka came within inches of adding Nancy's third of the evening early in the second half, curling his shot agonisingly over from the edge of the area.
The home side then started to take a grip on the game, but were still finding it tough to carve out any clear chances.
Nancy always looked a threat on the break, with the pace of Zerka and Youssouf Hadji a constant menace.
Hadji was denied by Smith with time running out and in time added-on Zerka wasted a glorious chance when played clean through a wilting home defence.