"Just this year we've met three teams with a better ranking than us: We beat England and Canada and drew against France," he said. "That gives us the self-confidence we can handle the best team in the world. That's also thinking we can go all the way. We can do it, we have the possibility."
Gerhardsson's side will get a strong early test against the U.S. on June 20 at Stade Oceania in Le Havre. "What I think is pretty good is that we meet them in the third game, so we have two games before we meet them," he said. "This is the first time for me (against the U.S.) but I know about the history, tough games during many years."
France coach Corinne Diacre is urging her players not to let the pressure of playing at home get to them.
The French have been drawn in Group A with South Korea, Norway and Nigeria. They open at Parc des Princes against South Korea on June 7.
"It should be an advantage and not a pressure to have the public behind us," said Diacre, who became the first woman to coach a professional men's team in France when she took charge of second-division Clermont in 2014.
Diacre tried to play down expectations and keep her players grounded.
"I don't know if it's a good draw, we'll see after the group stage," she said. "If we finish top of the group we know we can still come up against the United States in the quarterfinals. But that's the way it goes."
The draw is complete. Here are the final groups that will play next year at the Women's World Cup in France:
Group A is France, South Korea, Norway and Nigeria.
Group B is Germany, China, Spain and South Africa.
Group C is Australia, Italy, Brazil and Jamaica.
Group D is England, Scotland, Argentina and Japan.
Group E is Canada, Cameroon, Netherlands and New Zealand.
Group F: United States, Thailand, Chile and Sweden.
The United States has landed in Group F in the Women's World Cup draw on Saturday.
The defending World Cup champions will be joined in the group by Sweden. It is the fifth straight time the two opponents have been in the same group and the sixth time overall.
It will be a rematch of the Olympic quarterfinal in Brazil, where Sweden advanced on penalties after a 1-1 draw. Afterward U.S. goalkeeper Hope Solo called the Swedes "cowards" for focusing on defense. Solo was later suspended and U.S. Soccer terminated her contract.
Sweden is ranked No. 9 in the world in the latest FIFA rankings. The U.S. is ranked No. 1.
Former England defender Alex Scott is talking up her country's World Cup prospects under coach Phil Neville. Neville is the former Manchester United and England defender who played in three European Championships.
England was the surprise third-place finisher in the Women's World Cup in Canada in 2015. The team is ranked No. 4 in the FIFA world rankings.
Scott appeared in 140 matches for England from 2004-17.
Speaking on the stage at Saturday's draw, Scott says: "Bronze medal is good, but it's about turning that bronze one into gold and standing on that podium."
U.S. women's national team midfielder Carli Lloyd says she's confident the Americans will successfully defend their title next summer at the Women's World Cup.
Lloyd scored three goals in the final in the 2015 World Cup in Canada, and the United States defeated Japan 5-2 for their third overall championship in soccer's most prestigious tournament.
She was asked on stage at the draw event inside La Seine Musicale on Saturday how confident the U.S. team is heading into the tournament.
She said: "Pretty confident I must say. This squad is as talented as can be, we've got the depth and a great coaching staff in place."
The 24 teams that qualified for the Women's World Cup are set to learn their opponents for the tournament's group stage next summer in France.
Saturday's draw for soccer's most prestigious event is taking place inside La Seine Musicale, a dome-shaped concert hall perched over the river Seine on the outskirts of Paris. The draw is far enough away from the city center to not be affected by the widespread anti-government demonstrations taking place all day.
Those attending the draw include Carli Lloyd, who scored a hat trick for the United States in the final of the 2015 World Cup in Canada. The Americans defeated Japan 5-2 for their third overall World Cup title.