The soldier's death raised to 10 the number of French soldiers killed since France intervened in Mali.
AU official said the organisation is making progress towards a regional military force by end of 2015.
The mission said a car packed with explosives was driven up to the entrance of the UN base and detonated.
Police say they have identified the owner of the vehicle believed to have been used by the assailants.
Gunmen have freed four election workers a day after they were kidnapped in Mali.
The Malian army captain who led a coup in 2012 has apologised to the nation for his actions.