Alexandre Troester, 42, was killed and a German tourist and two Egyptians wounded on Saturday as robbers traded fire with police in the exchange bureau in the old souk, or market, of the town, a security official said.
The Sharm el-Sheikh shooting "did not target tourists specifically, but they were shot in random gunfire," Tourism Minister Munir Fakhri Abdel-Nur was quoted by the official MENA news agency as saying.
Troester was hit by two bullets and died before reaching hospital, French and Egyptian officials said.
Four masked men in cars opened fire after fleeing the scene when they were repulsed by security guards.
Security officials said three people were later arrested in connection with the attack.
Tucked between the mountains of the Sinai desert and waters of the Red Sea, Sharm el-Sheikh's glitzy strip of golden beaches, hotels and casinos, diving resorts and golf courses is a major player in Egypt's key tourism industry.
But the sector has suffered heavily since a popular revolt broke out a year ago that toppled president Hosni Mubarak in February.
The resort was a favourite bolt hole for Mubarak, who was known for showing off development in the area to foreign guests he invited there for political meetings and conferences.
MENA reported that hundreds of people on Sunday blocked a road leading to the souk in a protest over lack of security.