'Fit of madness'
Herve Morin, the French defence minister, said peacekeepers were "actively" searching for the man with the help of Chadian authorities.
The soldier had suffered a "fit of madness", but had not shown psychological problems in the past, he told France-Info radio.
UN agencies active in the Abeche region of Chad, where camps are home to about 450,000 Sudanese refugees and displaced Chadians, have ordered local staff to avoid travel because of the risk of running into the fleeing soldier.
"We have been asked not to move. We've warned our partners in the field," Annette Rehrl, from the UH High Commissioner for Refugees office in Abeche said.
The fugitive soldier and the two dead Legionaires were attached to European forces serving in Chad.
The dead Togolese soldier was part of a UN force taking over peacekeeping operations from the troops in the north African country.
France is Chad's former colonial ruler and still has about 2,100 troops in the central African nation.