Fulham said on their website (www.fulhamfc.com) that the deal for 26-year-old Seri included an option for a further 12 months.
Seri, who had also been linked to Chelsea and Borussia Dortmund, joined Nice in 2015 from Portuguese side Pacos de Ferreira.
"Jean Michaël arrives with Premier League qualities as well as great promise for the future, which is why he has been at the very top of our target list for a long time," said Fulham's director of football operations Tony Khan.
Le Marchand, 28, has played 81 matches for Nice, who finished eighth in Ligue 1 last season.
(Reporting by Alan Baldwin, editing by David Stamp)
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