Quick answer: Watch for the gold-ring scam, friendship-bracelet hustlers at Sacré-Cœur, the petition/clipboard distraction, and metro and tourist-site pickpockets.
Paris is safe, but a handful of well-known scams target tourists at the big sights. Knowing them is most of the battle.
Common scams to watch for
The gold ring
Someone ‘finds’ a gold ring near you and offers it to you, then demands money. Ignore and walk on.
Friendship bracelets
Men near Sacré-Cœur tie a bracelet on your wrist, then demand payment. Keep your hands in your pockets and don’t engage.
The petition / clipboard
People (often with a clipboard ‘for the deaf’) distract you for a signature while an accomplice picks your pocket. Say no and keep moving.
Metro & site pickpockets
Crowded line 1, the steps at Montmartre and the Eiffel Tower queues are pickpocket hotspots. Watch for staged jostling.
Three-card monte
Street gambling games near tourist spots are always rigged — never play.
How to protect yourself
Keep bags zipped and in front of you, don’t accept anything handed to you, decline petitions and games, and stay alert in crowds and on the metro. Use a cross-body bag and keep your phone away from café terraces by the street.