Bashir was indicted by the International Criminal Court last year for war crimes and crimes against humanity in Darfur, and could be arrested if he stepped foot in France, which is a staunch supporter of the ICC.
Sarkozy's office said Bashir would not be welcome.
"The president has indeed sent a letter to Omar Hassan al-Bashir to ask him to nominate the person who will represent Sudan at the Franco-African summit," said an official, making clear that the Sudanese leader himself could not come.
The summit had originally been set to take place in Egypt but France was concerned that Cairo would invite Bashir in person so reached a deal to switch the meeting to the French Riviera city of Nice, leaving Paris in charge of invitations.
Bashir had to cancel a trip to Turkey last year after Ankara came under pressure from the European Union not to host him because of the ICC indictment.
The United Nations estimates 300,000 Darfuris died and more than 2 million were driven from their homes following a 2003 rebellion, which was brutally suppressed.
Bashir, who was commander-in-chief of the armed forces during the conflict, is accused of torture and mass murder. he denies all charges of wrongdoing.
Sudan's state news agency SUNA said that in his letter to Bashir, Sarkozy had also expressed France's gratitude for the recent release of French hostages in the region.
Four French hostages were freed in the past two months in Darfur. Three were kidnapped in neighboring countries but aid sources said they were all being held in Darfur.
