The result makes the four teams of the group level on one point, following South Africa's 1-1 draw with Mexico earlier.
The 2006 World Cup runners-up France continued the poor form they showed in warm-up games and were lucky their opposition were too kind not to punish them.
Les Bleus played a better first-half and had two shy attempts through Sidney Govou, who missed from close range, and a Yoann Gourcuff freekick.
Uruguay's best chance came from hitman Diego Forlan who forced a fine save from Hugo Lloris.
Substitute go off
The second half was hardly a contest as both teams seemed to be struggling to create any danger.
France coach Raymond Domenech insisted on keeping the almost-absent Govou on the pitch, while Thierry Henry and Florent Malouda were on the bench, but even when the latter duo came on, nothing changed.
In the 62nd minute, Uruguay midfielder Nicolas Lodeiro was introduced, only to be booked three minutes later.
Ten minutes from time, Lodeiro, the youngest player in the Uruguay roster, received his marching orders after an imprudent challenge in Bacary Sagna.