Flyhalf Michalak picked up a shoulder injury while number eight Picamoles suffered a hip problem in the country's 30-0 defeat against the All Blacks in Christchurch on Saturday.
"Those two players cannot train this week and they will not be fit for Saturday's match. It has been agreed with team staff that they will travel back to France on Tuesday," the FFR said in a statement.
The FFR added that no players would be called up as replacements for the injured duo in what is effectively a dead rubber between the sides.
France, who lost the first Test in Auckland 23-13, complete the three-match series against the All Blacks in New Plymouth.