The 25-year-old French rider, who was second in the British MX1 championship, was preparing for the race in Cassel.
Lenoir was reportedly airlifted to hospital in Lille following the crash.
"The Honda Racing Family are sad to hear of the tragic loss of Steven Lenoir following a crash in Cassel," said 24MX Lucas Oil Honda, who Lenoir rode for in the MXGP last year.
"Our thoughts are with his family, friends, team and fans at this sad time."
British superbike rider Alex Lowes added: "Absolutely gutted, always gave everything he had on and off the track RIP mate."
Former British motocross champion Steven Lenoir has died after a crash during qualifying in France on Monday.