The creation in 2003 of the French Council of the Muslim Faith, known by its acronym CFCM, was seen as a crucial step in France's effort to address the concerns of one of Europe's largest Muslim communities.
Until the council was established, French Muslims had no way of communicating concerns or grievances to the government.
A total of 5230 imams, clerics and other Muslim officials from France's 1300 mosques voted on Sunday to select the council's national and regional leaders.
Delegates will meet on 26 June to elect a new executive council and president. Officials are nominated for two-year terms.
The council has been criticised as ineffective, in part because of internal power struggles.
France's Muslims are represented by numerous squabbling groups, associations and federations backed variously by Algeria, Morocco, Tunisia - former French colonies - or Pakistan.
Ayash Daraji, Aljazeera's correspondent in France, said the French authorities have tried to make the CFCM the sole representative of French Muslims.
"Unfortunately, the CFCM is divided among Algeria, Morocco and other Islamic tendencies. Thus, there have been two trends - the French government's one which wants a 'French Islam' and the trend of these divided groups"
French Islamic affairs expert
But they now fear that the organisation is bogged down amid rival political agendas.
Vincent Jissere, a French expert in Islamic affairs, told Aljazeera: "Unfortunately, the CFCM is divided among Algeria, Morocco and other Islamic tendencies. Thus, there have been two trends - the French government's one which wants a French Islam and the trend of these divided groups."
France's second religion
A conservative mosque network close to Morocco is fighting to keep its top position in the council, while the more liberal, Algerian-backed Mosque of Paris hopes to move up from third place.
Outgoing president Dalil Boubakeur is rector of the Mosque of Paris.
The Union of Islamic Organisations of France - inspired by Egypt's banned Islamist Muslim Brotherhood - made an unexpectedly strong showing in the 2003 election.
But it is expected to lose its status as the council's second-largest group in next Sunday's vote.
There are five million Muslims in France, making it the second religion in the country after Roman Catholicism.