Three big funfairs ( fête foraines ) take place in Paris each year. The season kicks off in late March with the Fête du Trône in the Bois de Vincennes (running until late May), followed by the funfair in the Tuileries gardens in mid-June to late August, with more than forty rides including a giant ferris wheel, and ending up with the Fête à Neu Neu, held nearthe Bois de Boulogne from early September to the beginning of October. Look up "Fêtes Populaires" under "Agendas" in Pariscope for details if you're in town at these times. 

Out of season, rue de Rivoli around St-Paul métro stop occasionally hosts a mini-fairground, and there's usually a merry-go-round at the Forum des Halles and beneath Tour St-Jacques at Châtelet. Merry-go-rounds for smaller children are to be found on place de la République, at the Rond-Point des Champs-Élysées by avenue Matignon, at place de la Nation, and at the base of the Montmartre funicular in place St-Pierre. The going rate for a ride is ?1.53