Investigators from the Serious Fraud Office (SFO) and French authority Parquet National Financier have informed the company of the investigation, they said on Thursday.
Director of the SFO, Nick Ephgrave, said: “Working collaboratively with our international partners is a crucial factor in the fight against international corruption.
“We will together rigorously pursue every avenue in our investigation into these serious allegations.”
Thales built the 650 so-called Lightweight Multirole Missiles (LMMs) that the UK announced it would supply to Ukraine in September, in a £162m order.
The firm also won a £1.8bn UK defence contract in February, which would see it maintain the Royal Navy’s fleet of ships and submarines for the next 15 years.
A Thales spokesperson said: “Thales confirms that the SFO and the PNF have commenced an investigation in relation to four of its entities in France and the UK.
“Thales is co-operating with the PNF in France and the SFO in the UK. The group complies with all national and international regulations.
“As the investigation is ongoing, Thales will not comment further.”
The firm also has premises in Belfast, Bristol, Cheadle Heath in Cheshire, Crawley in West Sussex, Doncaster, Ebbw Vale, Glasgow, Reading, Templecombe in Somerset.