Deschamps joined Beckenbauer and Zagallo as the only men to win the World Cup as a player and a coach.
The Football Association of Iceland had hoped Hallgrimsson would extend his contract for two more years.
World Cup winners France feature a number of players of African heritage.
The parade was under heavy police guard, with some of the 2,000 officers deployed in the capital to ensure the safety of the estimated 300,000 people who turned up.
Pussy Riot is most famous for performing an anti-Putin protest song in a central Moscow church in February 2012.
A crowd estimated at more than 100,000 thronged the capital's main square to see the players parade through the streets on an open-top bus.
The players arrived to a raucous welcome at Charles De Gaulle airport northeast of Paris.
More than 100,000 red-and-white-painted Croatian fans were expected to welcome the squad home later Monday in the capital Zagreb.
The 19-year-old is the poster boy for France's new crop of talent.
Over the past six weeks, 180 professionals appointed by the SC have been shadowing and observing the World Cup operation.
The 58-year-old's days as coach were numbered after his Lionel Messi-led side failed to fire in Russia.
Deschamps is just the third man to win the World Cup as a player and a coach.
Despite the decision, Dalic defended VAR as a "good thing for football".
The success has also led to a newfound feeling of togetherness in a country marked by years of often poisonous debate about immigration and French identity.
The 27-year-old ended the tournament with four goals as France won the title for the first time on foreign soil.