Lyon's women's team can win a fourth consecutive Champions League title when they face Barcelona in the final in Budapest on Saturday. As many as eight members of that team will be in the France squad in June and July when the country hosts the women's World Cup.
If they reach the late stages those players will be even more at home because the semi-finals and final will be played at Lyon's Groupama Stadium.
"We are in a virtuous circle with an audience that will come and watch," Aulas told AFP.
Aulas, an outspoken figure in French football for decades, said French women's football had benefitted from investment at first Montpellier and later Paris Saint-Germain, Bordeaux and Lyon, where his club took over a struggling women's team in the city in 2004.
"At a European level, we have probably provoked the desire in all the big clubs to be able to do the same thing, either by buying a club or by building a women's section integrated with the club.
"All four semi-finalists in the women's Champions League this season were major European clubs and the Lyon-Barcelona final is also testimony to Barca's determination to reach highest level."
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He said that while the Olympique Lyonnais women's team was run by the club's amateur section, its budget had steadily grown and this season was between seven and eight million euros ($7.8m and $9million). Women players at the club still earn far less than the men.
"There is a big difference between the men and the women but the evolution has been considerable. In Lyon, salaries (for women players) are between 5,000 and 10,000 euros per month."
However, among current OL players the FIFA women's player of the year Ada Hegerberg, Amandine Henry and Wendie Renard reportedly earn much more, as did former OL player, US international Alex Morgan.
"The best female players in the world can have salaries of up to 500,000 euros per year plus individual or collective image rights, as for Alex Morgan who had image contracts in the USA that could exceed one million dollars," Aulas said.
"The business almost breaks even and allows OL to win titles and also gain a considerable international reputation."
He said the crowds who come to watch Lyon's women's team were noticeably different from those who support the men's side.
"We have a slightly different and more family-friendly audience. There is less aggression," Aulas said. "Fans identify more with the national team even if at the OL we have managed to create our own fan groups."
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He added that the different atmosphere reflected differences in the way the game was played.
"The ball is in play longer in a women's game.
"There is probably less play-acting and it's probably easier to referee."
He said the World Cup will inevitably accelerate the development of women's football in France.
"It has to. It's going to be an incredible success. Most of the stadiums are already guaranteed huge crowds."
He said that hosting the later stages in Lyon had paid off even though "it was a gamble at the time that we bid for the games."
"In Lyon, the semi-finals and final will be sold out. We have 17,000 American reservations out of 59,000 tickets on sale for each of our three matches. The TV stations have acquired the rights, which are more modest than for the men. We are in a virtuous circle with an audience that comes to matches."
He added that women's football in France is attracting advertising from some of the country's biggest companies who were "more oriented towards rugby, in particular, and are now turning to women's football".
And he made the bold prediction that "broadcasting revenues from advertising will be very similar to what they were for Euro 2016 or the World Cup."
Aulas said it would give French football a huge boost if Les Bleues could win as hosts.
"They have the capacity to do so. France's men are world champions. It would be historic to have women win in the same cycle.
"The planets are aligned for this national team and believe they can win the final."
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