Fournier was installed as Lyon's coach on Friday for the next two seasons, replacing Remi Garde, who decided to take a break from football.
At his first press conference as Lyon boss, Fournier declared Gonalons, who has been heavily linked to Napoli, would be his key man and urged his new employers not to sell the 25-year-old to the Serie A club.
"Gonalons is the player on whom the future of the club should be built, and on whom I would like to rely," Fournier said on Friday.
"But in the end I'm not the one who makes the decisions and in theory a big offer can always come in.
"But I'm going to call him and let him know that I'll be expecting him here rain or shine on the first day of training."
Gonalons made 54 appearances in all competitions for Lyon in 2013/14, as they finished fifth in Ligue 1 and reached the quarter-finals of the UEFA Europa League.
The Lyon youth product has also reportedly attracted the attention of Arsenal and Manchester United.
Like his predecessor, Fournier played for Lyon, although he was never a team-mate of Garde's.
The 46-year-old coach moved to the Stade de Gerland from Reims, who he led from Ligue 2 into Ligue 1 at the end of the 2011/12 season, while they finished 11th under his leadership in the 2013/14 campaign.
"I'm thrilled to be here, and I'd like to thank the president (Jean-Michel Aulas) and (his advisor) Bernard (Lacombe)," Fournier said.
"I'm happy that the club talked to a lot of coaches; it really legitimises my appointment. I'm glad that I have this opportunity to embark on a really exciting project.
"I'll have a few days' holiday but I can't wait to get stuck into the job. It will be a complicated season but we'll do all we can to make sure it's a successful one."
Fournier praised Garde's work during his three seasons in charge but explained he plans to make some changes.
"The work that Remi did set a very high standard," Fournier said.
"But I've got a few ideas and a different methodology, and my arrival should allow a new impetus at the club - and change a few old habits."
