"An analysis did not show alcohol in the driver," said prosecutor Olivier Elsig, adding that there were also "no elements backing the hypothesis of a cardiac problem or illness."
As a result, the theory that an unwell driver was the cause of the accident is "a little less credible".
Investigators were working initially on three hypotheses for the accident, including the possibility that the driver fell ill, technical problems with vehicle and human error.
Probes were ongoing on the two remaining theories, Elsig said.
Addressing media speculation that the driver may have been distracted as he was putting on a DVD, Elsig said: "At the moment I have no witness account from a child or anyone who have seen the driver handling a DVD or anything else."
He also confirmed that the driver, whose identity has not been disclosed, was not speeding, saying he was driving at "below the authorised speed in the tunnel".
"Speed is not at all a cause of the accident," the prosecutor said.