The U.S. State Department has accused Syria of failing to protect the embassy and demanded compensation for the damage. No one was injured in the incident.
At the French embassy, the guards fired into the air after the personnel were injured in a similar attack, officials say.
The incidents come after the U.S. and French ambassadors visited the restive city of Hama Central last week.
The separate visits - the two governments said were intended to express solidarity with the anti-government protesters - has drawn sharp criticism from Damascus.
Pro-government demonstrators took part in demonstrations outside the embassy for two days.
The French Foreign Ministry said three of its employees was injured when protesters attacked the French embassy on Monday.
Security guards fired warning shots "to prevent multiple intrusions into the enclosure," ministry spokesman Bernard Valero said.
The attack, he added, was in violation of international law. "It is not with illegal methods such as the Syrian authorities divert attention from the fundamental problem, which is to stop the repression of the Syrian population," Mr Valero said.
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