Mark McGhee's side produced a battling display in their first European encounter for 13 years with Pascal Berenguer's header proving to be the only difference between the two sides.
McGhee brought Bob Malcolm back into his starting line-up for the first time since the opening day of the season instead of Chris Porter with Marc Fitzpatrick replacing Steven McGarry in midfield.
The French side started brightly and pressed the Steelmen back for long spells with Graeme Smith being forced to get down well to save Mosef Zerka's header.
In a rare Motherwell attack Stephen Hughes almost latched on to John Sutton's ball forward but Nancy keeper Gennaro Bracigliano raced off his line to clear the danger.
Nancy's dominance finally paid dividends three minutes before the interval when Berenguer headed home Jean Calve's cross and they should really have added to their advantage in a one-sided second period.
Issiar Dia and Julien Feret both went close to adding a second goal but the best chance fell to Dia who saw his 72nd-minute spot-kick superbly saved by Smith after Mark Reynolds had brought down Feret.
But Motherwell are still in the tie and could make home advantage count next month when the two teams meet in the second leg at Fir Park.