Five detonations or shots were heard by millions on live television while Mr Brandet spoke to reporters as police stormed the home.
"Negotiations were opened but it became clear that they would not succeed and police then entered the home, where they found the body of a woman," Mr Brandet said.
Police sources said the attacker, who has not been named, was a former soldier and a neighbour of the couple.
Some sources described the attacker as a neighbour of the policeman, who was in plain clothes when he was killed. Witnesses heard the assailant, described as a teenager or in his early 20s, shout "Allahu Akhbar", Arabic for God is great.
However, the local prosecutor, Vincent Lesclous, said the killing was being treated as a criminal case rather than terrorism.