Swiss and Dutch planes came as close as 15 seconds to colliding over France on Wednesday, airline officials say.
The two flights were reportedly within 300m of the other when pilots and onboard warning systems averted a crash over the northern city of Rheims.
Rheims air traffic controllers were in charge of the planes, which were flying at a reported 9,500m.
France has launched an inquiry to find out if human error or technical failure was to blame.
A French aviation spokeswoman said the near-miss was not related to the three-day strike by Paris air traffic controllers - which has just ended.
The incident occurred at 0645GMT.
The Swiss International Air Lines flight was carrying 137 passengers and 11 crew from Zurich to New York.
Seventy five passengers and five crew members were aboard the KLM flight from Geneva to Amsterdam, a KLM spokesman said.
"The autopilot indicated that intervention was needed and at the same time the KLM pilot saw the Swiss plane and made a sharp left turn and averted a collision."
"They were about 300m apart," he said.
A spokeswoman for France's civil aviation authority (DGAC), said the planes came within 15 to 35 seconds of colliding.
In 2002, there were 59 near-misses in French air
space, but the collision-avoidance systems prevented
crashes, said the DGAC spokeswoman.
The same year 71 people died in a mid-air collision between a Russian airliner
and a cargo plane over southern Germany.