The 32-year-old was making his debut at the TT after recovering from a serious accident at last year's North West 200.
The organisers of the event passed on "their deepest sympathy to Franck's family and friends".
Petricola died at Sulby Crossroads, becoming the 141st fatality at the races since they began in 1907.
Organisers added that the coroner of inquests had been informed and an investigation was under way.
Clerk of the course Gary Thompson said: "Franck showed incredible character to battle back from the serious injuries he suffered at the North West 200 last year when many a lesser man would have given up.
"It showed his determination to compete on the mountain course."
"The road racing community has lost a remarkable man and I extend my deepest sympathy to his family and friends."
Two riders were killed during last year's festival.
Petricola suffered multiple fractures and a head injury after crashing in practice at the North West 200 in Northern Ireland in 2014 and was in a coma for several days.
He was flown home after the meeting but made a full recovery and raced at the event just last month.
Speaking about his 2014 crash earlier this year, he said: "I don't remember why I crashed but I accept it. I am a big boy.
"When you ride in a road race you know it is possible to have a hard crash like this. It is not a problem."
Practice week continues on Thursday night, with the first race of this year's event held on Saturday.
French rider Franck Petricola has died following an accident during a qualifying session on Wednesday at the Isle of Man TT Races.