Police fired tear gas and water cannon as the protests turned violent after weeks of relative calm, during which marches had attracted declining numbers of participants.
A Banque Tarneaud branch spewed flames before firefighters arrived and rescued a woman and her infant from the building, with 11 suffering minor injuries, the fire department said.
Rioters also set fire to an upmarket handbag store and two newsstands on the Champs Elysees, while scattered bonfires burned on the thoroughfare.
Protesters hurled cobblestones at riot police through clouds of tear gas in front of the Arc de Triomphe monument, which was ransacked at the peak of the protests in December.
Police arrested nearly 240 protesters as rioters looted stores around the Champs Elysees and wrecked the high-end Fouquet's restaurant.