The French took care of stragglers on the march is an orderlyh fashion, stationing picked officers at certain points to herd them along. This doesn't apply to deserters, but to those who fell out during the long and sometimes forced marches that the Grande Armee made. An example would be Davout's forced march to Austerlitz in December 1805. A large portion of Friant's division crapped out along the line of march, but were picked up, caught up, and rejoined the division when they caught their breath.

Sincerely,
Kevin