Abily began her football career joining Jeanne d'Arc Bruz in 1992. In 1994, she joined nearby club FC Bruz. After a year's stint at another local club, Abily spent time in the first division playing for Stade Briochin and La Roche-sur-Yon. In 2002, she was selected to attend the women's section of the nationally recognized Clairefontaine academy. After her stint at Clairefontaine, Abily signed with Montpellier and won two league titles while at the club, as well as the Challenge de France, the women's domestic cup. After three seasons with Montpellier, Abily joined Lyon. Similar to her stint at Montpellier, she won several titles, which included three straight league titles from 2006–2009. In 2008, Abily joined the new United States-based women's soccer league, Women's Professional Soccer, after her American playing rights were chosen by the Los Angeles Sol in the 2008 WPS International Draft. After helping the Sol win the league, Abily returned to France where she played for Paris Saint-Germain on loan. In 2010, she returned to the United States to play with FC Gold Pride and, subsequently, won her second consecutive title in the league. In 2010, Abily announced that she would be returning to Lyon for the 2010–11 season and, subsequently, was a part of the team that won the 2010–11 UEFA Women's Champions League.
Abily is also a French international. Prior to playing for the senior team, she played at youth level representing the under-18 team at the 2001 UEFA Women's Under-18 Championship. Abily made her senior international debut in September 2001 in a friendly match against the Netherlands. She scored her first goal for the national team six years later in a 2–0 win over China in February 2007. Abily made her major international tournament debut for the team at UEFA Women's Euro 2005 and later played on the teams that qualified for UEFA Women's Euro 2009 and the 2011 FIFA Women's World Cup.
Abily has won the league with her respective club on four occasions. She won two titles with Montpellier and back-to-back titles with Lyon. During two of those title runs, she was selected as the Female Player of the Year in 2006 and 2007. In 2010 she won the WPS Championship with the FC Gold Pride.