"Investigators from the SFO and French authority Parquet National Financier (PNF) have informed the company of the investigation," it said, noting the two agencies were probing "in their respective jurisdictions".
Thales has its headquarters in Paris. Thales UK is a subsidiary and one of the British government's key defence contractors, employing over 7,000 staff at 16 sites across the country.
It built hundreds of lightweight missiles which the UK sent to Ukraine in September.
A Thales spokesperson confirmed that the SFO and the PNF had "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 SFO announcement follows police in France, the Netherlands and Spain searching the multinational's offices in June, over suspicions of corruption linked to arms sales, according to reports.
SFO director Nick Ephgrave said he hoped the joint probe would reinforce the SFO's and PNF's "long-standing relationship, built on mutual cooperation and shared success".
"We will together rigorously pursue every avenue in our investigation into these serious allegations," he added in a statement, which did not provide any further details about the accusations.
The SFO is a specialist prosecuting authority tackling top level serious or complex fraud, bribery and corruption, in England, Wales and Northern Ireland.
Thales specialises in defence electronics, and built the 650 so-called Lightweight Multirole Missiles (LMMs) that the UK announced it would supply to Ukraine in September, costing GBP 162 million ($204 million).
The firm also won a GBP 1.8-billion UK defence contract in February, which will see it maintain the Royal Navy's fleet of ships and submarines for the next 15 years.
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