I was in Paris just last week (May, 2002) and I saw a new scam. Many areas where flooded with young people with clipboards. They pretend to be deaf/mute. They ask for you to sign a petition. Then they flip over their paper or clipboard to show you that you owe them money - 2, 3, 10 euros. We were riding the funicular near Sacre-Coeur later with 5 of these girls and they were merrily chatting away with no difficulty. Later we saw the same girls pretending to be deaf/mutes!
Just ignore them, say "No" and walk past. As always, watch for pickpockets.
I encountered these people everywhere - near the Louvre, on the bridges over the Seine and in Montmatre.