Applications for French passports among Britons more than trebled to 1,300 in 2016, then more than doubled in 2017.
The latest ranking was compiled by the Henley Passport Index, which takes global mobility into account and is based on exclusive data from the International Air Transport Association (IATA).
The Henley Passport Index warned that Britain’s ranking could get even worse in the years to come.
“Throughout most of the index’s history, the UK has held one of the top five places in the ranking,” it said.
“However, with its exit from the EU now imminent, the UK’s once-strong position looks increasingly uncertain.
“The Brexit process has not yet had a direct impact on the UK’s ranking, but new research using exclusive historical data from the Henley Passport Index indicates that this could change, with consequences that extend beyond a decline in passport power.”
Dr Christian H Kaelin, chairman of Henley & Partners and the creator of the passport index concept, said: “This latest research appears to confirm something that many of us already knew intuitively: that increased visa-openness benefits the entire global community, and not just the strongest countries.”