Georges began her football career playing for her hometown club Paris Saint-Germain at the age of 12. She spent six years in the club's youth academy before being accepted to CNFE Clairefontaine, the women's section of the Clairefontaine academy. Georges returned to Paris Saint-Germain after a year at Clairefontaine and was promoted to the senior team for the 2003–04 season. She made 19 appearances with the team scoring one goal. After the league season with Paris Saint-Germain, Georges announced her intentions to move to the United States to attend Boston College. She majored in marketing and, while at the university, played college soccer for the Boston College Eagles women's soccer team. In her first season, Georges featured in 13 matches making nine starts. In her second season with the team, despite missing matches due to representing France internationally, she was named to the All-ACC first team and also earned third-team All-America honors from the NSCAA. In her final season at the university, Georges was named to the conference's first team for the second consecutive season and was awarded the ACC Defensive Player of the Year award. She was also a semifinalist for the prestigious Hermann Trophy.
Lyon
Following the conclusion of her amateur career, Georges returned to France to join Olympique Lyonnais. In her first season with the club, she was penciled in as a starter featuring in 18 matches as Lyon finished the season as champions after going undefeated. Georges was also influential in the team's Challenge de France campaign featuring in all four matches, including the final, which Lyon won, defeating her former club Paris Saint-Germain 3–0. In the 2008–09 season, Lyon were again crowned champions. In the season, Georges scored her first career goal for Lyon in the opening league match of the season against Paris Saint-Germain. She also helped the club reach the semi-finals in both the domestic cup and UEFA Women's Cup. Following the departure of veterans Camille Abily and Sonia Bompastor to the WPS, Georges was handed the captaincy by coach Farid Benstiti for the 2009–10. She played in 16 league matches as Lyon were declared champions for the fourth consecutive season. In Europe, Georges was a part of the Lyon team that reached the 2010 UEFA Women's Champions League Final. The team, however, lost 7–6 on penalties to German club Turbine Potsdam. In the next season, despite the return of Abily and Bompastor, Georges remained captain and displayed her leadership by leading Lyon to victory in the UEFA Women's Champions League Final.
