Armed Robbers Steal Cash, Jewels in Cannes Home Invasion of CEO Shahab Elmi

Shahab Elmi -- CEO of the supplement company Cymbiotika -- was robbed at gunpoint in France this week in a home invasion where thieves made off with a small fortune ... sources connected to the situation tell TMZ.

We're told early Thursday morning, robbers broke into the home Elmi was staying in with his wife, Durana, and their two young daughters in Cannes. Our sources say ... the suspects were armed, including one who wielded an SK-style machine gun and held it to Elmi's head during the home invasion.

According to a local outlet, there were three robbers -- all hooded and masked -- who broke in around 3:30 AM.

The thieves reportedly nabbed more than $200K in cash, plus other jewelry and valuables ... which we're told totaled several hundreds of thousands of dollars.

The California Post was first to report on the story.

Our sources say the family is fine but "traumatized" ... with Elmi and his wife spending time with their kids to help them cope with everything.

Elmi and his family had been renting the home for the Cannes Lions International Festival. His company was reportedly appearing at multiple events for the festival.