I've taken my fiancée to Paris twice - first for our 1st anniversary, and again for our 4th - and both times we had troubles with guys bothering us around the Sacré Coeur in Montmartre. They hang around the front entrance to the park and pester tourists with some sort of strange scheme involving tying string to people's fingers. From what I can tell, anyone who's ensnared by the trick ends up being pestered into buying a bit of wool for a few euros.
Often we managed to get past them immediately by saying no, but in some cases they were persistent, and in a few cases they continually grabbed us and continued to shout at us after we escaped. In one case I had to physically pull one of them off my fiancée, as he was gripping her arm tightly and trying to tie string to her hand. Not exactly enjoyable when we're trying to have a relaxing holiday. In the end we resorted to walking up the long set of stairs to the left of the park and coming back down through the top entrance, which was exhausting and left us uncomfortable in the heat.
One thing I noticed is that the police periodically appear, and the sellers run off or hide down side roads. In once case we were treated to the sight of three armed officers chasing after one of them and tackling him to the ground, much the the enjoyment of everyone watching.
So, what's the deal with these guys? Are they breaking the law by being there? What's the best way to deal with them? We love everything about Paris, especially the Sacré Coeur, but these guys are an annoyance we'd prefer to avoid.