The arrests followed a raid on the French firms offices across the UK as well as residential addresses.
The SFO said in a statement it believed bribes had been paid in order to win foreign contracts.
SFO Director Richard Alderman said: "The SFO is committed to tackling corruption. We are working closely with other criminal justice organisations across the world and are taking steps to encourage companies to report any suspicions of corruption, either within their own business or by other companies or individuals."
A task force of around 150 SFO officers and police were involved in the raids.