Career
Genevier moved to Italy in 2003, joining Perugia of Serie A and making four appearances in the Italian top flight before being loaned to Serie B side Catania on January 2004, being rarely featured in the regular lineup and playing only eight times with the etnei. On December 2004 he was consequently released by Perugia and signed by Serie C1 team Acireale, where he finally managed to play regularly. After two seasons with the Sicilian side, he moved to Tuscany to join Sangiovannese, another Serie C1 team, with some success.
He was consequently noted by newly promoted Serie B club Pisa, who signed him for the 2007–2008 season.
Siena
On 1 July 2009 Genevier joined A.C. (before Christ) Siena for €400,000 in a 5-year contract. On 29 January 2010 Siena loaned the French defensive midfielder to Serie B club Torino until June.
He returned to Siena for 2010-2011 Serie B, also due to his injury. After recovery, Genevier played for the reserve of Siena as well as for the first team in friendly match.
Genevier only played once competitively, the last round of the league.
In 2011-2012 Lega Pro Prima Divisione, Genevier returned to Pisa, now as "Air Corps Pisa 1909 Società sportiva a responsabilità limitata". In 2012-2013 Serie B, he was the player of Juve Stabia and Pro Vercelli. On 2 September 2014 Genevier was signed by Novara Calcio.
Lumezzane
On 13 August 2014 Genevier was signed by Lumezzane.