The climbdown came after checks on passenger lists failed to turn up any "terror links".
A spokeswoman at the French prime minister's office said on Thursday that no formal inquiry was under way.
She added no arrests had been made in connection with Wednesday's cancellation of the flights between Paris and Los Angeles.
"We have not detected passengers with the profile of people belonging to a radical Islamic group," a source close to French investigating judges that deal with terrorism said. "All the checks so far have come to nothing."
France's DST counter-intelligence service checked passenger lists of US-bound Christmas flights after a tip-off from US intelligence.
A US official said "credible, reliable" intelligence reports had been relayed to France saying "extremist" groups were planning "near-term simultaneous attacks" that could be on a scale of the September 11 attacks.
The DST questioned a number of people, but found no evidence of members of radical Islamist groups among them.
The only person named by US Intelligence as a suspect, a Tunisian man with a pilot's licence, was still in Tunisia and had no apparent plans to leave the country.
"There were people who were felt to pose a risk, in terms of being possible al-Qaida supporters, because of the countries they had visited. Because of the end-year security alert, the US authorities didn't want to take any risks"
International Terrorism Observatory
French Prime Minister Jean-Pierre Raffarin decided to cancel the flights in question, even though the DST's checks were negative, in order to eliminate any trace of risk.
The head of the International Terrorism Observatory in Paris, Roland Jacquard, also said the flights had been cancelled as a precaution.
"There were people who were felt to pose a risk, in terms of being possible al-Qaida supporters, because of the countries they had visited. Because of the end-year security alert, the US authorities didn't want to take any risks," Jacquard said.
"But it's supposition. There may well be more checks on these people, inquiries may be started, but we are not at the operational stage, so to speak."
An Air France spokeswoman said flights to Los Angeles would resume on Friday as normal.
Two flights were due to leave Paris on Friday - one at midday and the second in the evening. Two return flights from Los Angeles to Paris were also to depart as normal, she said.