Charles Prow, 23, was injured when part of the stage roof collapsed onto a number of crew on Thursday.
A French worker was killed immediately in the accident at Marseille's Stade Velodrome - the city's main football ground - which led to the singer's planned concert on Sunday being cancelled.
Mr Prow died during the night in the neurosurgery unit at Marseille's La Timone hospital after suffering injuries in a fall of nearly 50ft (15m), a local newspaper said.
Two other workers, one British and one American, remain in a serious condition, it said.
It is thought the victims were on the stage while the roof was being raised by four electric winches on metal columns at the corners of the stage.
Early reports suggest that one of these columns, which were held up by cranes, collapsed, causing the roof to fall.
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