Galtier joined Nice ahead of the 2021-2022 campaign after winning the Ligue 1 title with Lille, but he stayed at the Allianz Riviera for just one year before making the move to PSG.
Speaking on RMC show 'After Foot', ex-Nice director of football Fournier suggested Galtier's exit came down to more than just football reasons.
"It's common knowledge that the relationship I had with Christophe was quite chaotic from the start of the season," said Fournier, who himself left for Parma in July
"Quite honestly, if I explain the real reasons we argued, Christophe would no longer be allowed in a locker room, neither in France nor in Europe.
"But it was not about football matters. These are much more serious things from my point of view. It was indirectly linked to football. These are things that affect me deeply.
"We finished the season and we, him and I, were as professional as possible to limit the negative impact that it could have had on the team. Then there was the separation."
Galtier was asked about those remarks at a pre-match press conference on Thursday ahead of his first meeting with Nice since joining PSG.
"He is pretentious," Galtier said. "I am not surprised at the way he expressed himself. I don't want to get tired of debating on everything that was said.
"If we do that, the way it works means we create one debate after another. I'm not surprised about what I heard knowing the character. That's all I've got to say."
Galtier won 23 of his 43 matches in charge of Nice last season and guided the club to a fifth-place finish in Ligue 1.
He departed with the best points-per-game record of any coach in Nice's Ligue 1 history, with his return of 1.76 marginally better than current incumbent Lucien Favre's 1.67.
Galtier's Nice went unbeaten against PSG last season and were the only side to keep clean sheets in both matches against the Parisian side.
However, PSG welcomes the Eagles to Parc des Princes on Sunday having won seven of its opening eight matches, scoring 26 goals and conceding only four in the process.
Asked if his side are prepared for the challenge on the back of a two-week international break, Galtier said: "We have to get back to normal as quickly as possible.
"We've worked for the past 10 days with five players. This is the first game in a long series. There are 13 games to go before the World Cup and we are preparing carefully."