Police said fighting broke out on the Champs Elysees and Hollande and Interior Minister Manuel Valls left as soon as the World War I commemoration ceremony ended, Radio France Internationale reported.
Witnesses said there were several groups of protesters.
Police said about 70 people were arrested.
The police chief for the area said protesters responded to a call from Printemps Francais, one of several groups that have protested against same-sex marriages and adoptions, and other right-wing groups, including Renouveau Francais.
The leader of the Bonnet Rouge movement condemned any disruption of the ceremony in advance as as reports of such protests surfaced on social networks, RFI said.
This year's ceremony was part of a planned year of commemorations for the centenary of the 1914-1918 war.