The woman, named Isabelle Prime, was abducted on the way to work, reported French channel BFM TV. She was taken by six men dressed as policemen, while her driver escaped.
In a statement sent to AFP on Thursday, Jean-Noel Prime, the father of the kidnapped woman said: “We face up to this challenge with confidence, and we are staying close to the French authorities with whom we are in permanent contact and who we know are determined to see our daughter set free.”
Prime herself was well aware of the danger of the area, telling a French newspaper last year: “Yemen is not a country at war, but there is a constant risk of attack, so we need to have armed guards.”
Yemen has descended into chaos since Shiite Huthi militia swept into Sanaa from their mountain stronghold in the north last year, eventually prompting the president and prime minister to resign.
French President François Hollande called for the woman to be released “as soon as possible”, adding that authorities were working to locate her.
A number of Western nationals have been taken hostage in Yemen in recent years. In December, US journalist Luke Somers and South African teacher Pierre Korkie were killed by Al-Qaeda militants in the southern Shabwa region during a failed US-Yemeni rescue bid.