The cemetery in the town of Loos-en-Gohelle in the Pas-de-Calais region holds the remains of British and Canadian soldiers killed in a battle there in October 1915.
Vandals covered 12 graves and a monument in pink swastikas.
Mr Sarkozy wrote the Queen a letter to express his "indignation" at the desecration.
"I condemn with the greatest firmness this odious act and ask you to convey my emotion and that of the French people, sympathy and solidarity, to the families concerned and to all the British people," Mr Sarkozy wrote.
France's minister for veterans, Hubert Falco, said that the desecration, which took place before dawn, was "an insult to the memory" of the soldiers and an "insult to France".
Last month, vandals smashed crosses and monuments on the graves of 95 German soldiers in a joint military cemetery in eastern France where the German and French soldiers who fought against each other in the First and Second World Wars are buried.