Paris Saint-Germain midfielder Geyoro, winning her 50th cap, became the first player in tournament history to score three times before half-time, with Les Bleues' five goals heading into the interval also a record.
In an explosive performance that only solidifies their credentials as one of the pre-tournament favourites, France extended their winning run to 15 games across all competitions to go top of Group D after the first round of fixtures.
Geyoro's opener in the ninth minute set the tone for a superb first half at New York Stadium, with Marie-Antoinette Katoto doubling the lead three minutes later, before Delphine Cascarino sparked a madcap stretch before the interval that saw her team-mate grab her second and then third.
That kept a full contingent of players on to help seize a late consolation goal through substitute Martina Piemonte, but Milena Bertolini's side now face a serious test of their character.