The number one problem why a new Papillon owner would get frustrated.
All Toy dogs are somewhat hard to house train; Papillons are no different than all the other small dogs.
While some Papillons learn the concept of doing their thing outside quickly, others can be more difficult in this matter.
So, here we have first to understand the "why" and look and think from such a small dog's perspective.
First, the genes of small dogs are most likely different, their instinct to go outside is much lesser than from a big dog. Five hundred years plus, they have gotten away to piddle in the corners, and do their mini poops in another corner, and people had "put up" with it, and lived with it. If it had been a Bull mastiff, or a Great Dane, the owners of the castles, and residences would have given up the dog, there would have been no breeding of these dogs. People bred only dogs who understood that concept very quickly.
Little dogs accidents were so much easier to live with, so small dogs were reproduced for generations with their little accidents, hence, today, small dogs do not have that instinct much in mind, as their big relatives have.