Everybody is asking this at this time in the year (here in the USA).
Of course they do, just like all other canines (if they got hair to shed).
But....a.true to breed Papillon has no undercoat; so, this will have a big effect of the amount of hair he is shedding. And if you brush regularly, the hair will go on the brush, and not on your clothes or couch!!
Brolle