The embassy released a statement Friday night urging Americans to report suspicious activities and stay away from any security incidents.
It also noted that French authorities have increased the terrorism alert level in recent months since attacks in January in Paris left 17 victims and three Islamic attackers dead, so there are more troops and police in the streets than in previous years.
And French prosecutors say the suspect who they believe attacked a U.S. gas plant in France is a local truck driver who was known to workers at the Air Products plant.
Paris Prosecutor Francois Molins said Friday that the suspect, his wife, sister and another person who he would not describe further were in custody. He said the man found decapitated at the factory on Friday was the boss of the transportation company that the driver worked for in southeastern France.
Prosecutors' spokeswoman Agnes Thibault-Lecuivre told The Associated Press they haven't started asking questions about what might have motivated the attack and says it's too early to say whether there could be a connection to international terror groups.