If replicated, it would leave Mr Zemmour, a polemicist talk show host, facing incumbent Emmanuel Macron in a run-off for the French presidency.
The rise of Mr Zemmour in opinion polls has rocked long-held expectations that the vote would be a rerun of 2017's contest between Mr Macron and perennial far-right National Rally figure Ms Le Pen.
Friday's poll by Ipsos Sopra Steria for French newspaper Le Monde is the second to put Mr Zemmour in the run-off vote. He has not officially announced his candidacy but has described himself as a “candidate in the debate” and is widely expected to run.
The survey of 16,000 people interviewed from 7-13 October put him on 16-16.5 per cent of first-round votes, compared with 15-16 per cent for Ms Le Pen.
Mr Macron still led the first round with 24-28 per cent.
The poll did not predict the second round outcome, but other polls have forecast Mr Macron as the ultimate winner.
Pollsters noted that Mr Zemmour, who holds convictions for inciting racial hatred, was more divisive among voters than Ms Le Pen. Only 20 per cent consider he has what it takes to be president, compared with 30 per cent for the National Rally leader.
The 63-year-old pundit and writer made a name for himself by making controversial claims about the causes of perceived ills of modern French life. He has claimed that French identity has been destroyed by immigration, feminism, homosexuality, Europe and free trade, among other things.
He has drawn comparison with Donald Trump for his outlook and political approach – having boasted about the crowds he draws to his rallies – but is seen as more articulate in interviews and debates.
Polling found that 65 per cent of people who said they would vote for Mr Zemmour said they were “radical” or “very radical”, more than double the figure for the wider French public.
Almost all (98 per cent) said France should be further closed to immigration and 96 per cent said they consider Islam a threat to the country. Only 12 per cent were concerned with the environment and 7 per cent with social inequality.
Just over half of those who backed him in the poll were supporters of Ms Le Pen last year.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies