A report said there was still "much uncertainty", but fenugreek seeds imported in 2009 and 2010 "had been implicated in both outbreaks".
More than 4,000 people were infected during the German outbreak, 48 died.
Investigators traced the source back to a bean sprout farm in Bienenbuettel, Lower Saxony.
The outbreak in Bordeaux affected 15 people and was linked to seeds sold by a firm in the UK - Thompson and Morgan, although it said there was no evidence of a link.
Linked Both outbreaks involved the rare strain of E. coli known as O104:H4.
The European Centre for Disease Prevention and Control (ECDC) said the strain was so rare in humans the outbreaks were unlikely to have been isolated incidents and both were linked to eating sprouting seeds.
Food Standards Agency advice
- Do not eat sprouted seeds such as alfalfa, mung beans (or bean sprouts) and fenugreek raw
- Cook sprouted seeds until steaming hot throughout
- Clean equipment used for sprouting seeds
- Wash hands after handling seeds intended for planting or sprouting
Further investigations have been trying to determine if the source of the infection was contamination at the sites, or if they had been supplied with contaminated seeds.The report said the German outbreak had come from seeds imported from Egypt in 2010. The outbreak in Bordeaux was linked to seeds exported in 2009 from Egypt to the UK and then sold to France.
Seeds from the UK company Thompson and Morgan are being tested by the Food Standards Agency.
In a statement the firm said: "We can confirm that our own supplier sourced this Egyptian seed, which was then supplied to us.
"Further, we can confirm that this sprouting seed was then exclusively supplied into the French garden centre market."
The report added there could be more outbreaks of the deadly E. coli as "other batches of potentially contaminated seeds are still available within the European Union and perhaps outside".
The ECDC and the European Food Safety Authority "strongly recommend advising consumers not to grow sprouts for their own consumption and not to eat sprouts or sprouted seeds unless they have been cooked thoroughly" until their investigations are complete.