With drums beating, carhorns blaring and cries of “Vive l’Algérie!”, fans danced in the streets of parts of the French capital and outlying towns, many converging on the Champs Elysées.
People of Algerian origin make up France’s largest immigrant community and the crowds were out in other towns and cities, notable Lyon in the centre of the country, Marseille in the south and Lille and Roubaix in the north-west.
Some fans clashed with police in Paris, Marseille and Lyon.
Police fired teargas in all the cities and 74 arrests were made across the country.
In Lyon police used water-cannon to prevent the crowd spilling over into shopping areas and a number of cars and dustbins were set alight.
No serious injuries have been reported.
In Algiers thousands of people, both men and women, converged on the city centre, playing flutes and tambourines, while fireworks were let off and boats sounded their sirens, and there were similar scenes in the eastern city of Constantine.
On Sunday, when Algeria beat South Korea, 28 people were arrested during boisterous celebrations.
Far-right activists seized on Sunday’s incidents to portray Algerian fans as thugs and casting doubt on the fans’ loyalty to France on social media.
Some of their claims proved to be inaccurate, notably a claim that a church had been subject to an arson attack in Lyon and a photo of an apartment block covered in Algerian flags that was said to be in Paris but was in fact in Algiers.
Sporting affiliation and patriotism are not just of interest to tweeters from France’s Front National and hardline nationalist groups such as Bloc Identitaire.
In a recent column US right-wing columnist Anne Coulter judges a growing interest in “soccer” there “a sign of nation's moral decay”.
“I promise you: No American whose great-grandfather was born here is watching soccer,” she writes.
In 1990 British Conservative politician Norman Tebbit applied the loyalty test to a different sport.
"A large proportion of Britain's Asian population fail to pass the cricket test. Which side do they cheer for? It's an interesting test. Are you still harking back to where you came from or where you are?" he told the Los Angeles Times.