Lamouchi, the first coaching casualty of the tournament, was appointed in January on a contract until 2028. He leaves the post with matches to come against Japan on Saturday and the Netherlands on June 25.
Tunisia won just one of their five games under Lamouchi, beating Haiti 1-0 in March, while losing 1-0 to Austria and being thrashed 5-0 by Belgium in a pair of World Cup warm-up matches this month.
In a statement on social media on Tuesday, the TFT said Renard would take charge until the end of Tunisia's World Cup campaign.
"The agreement also stipulates that negotiations will be opened after the World Cup campaign to consider a long-term partnership based on specific sporting objectives," it added.
The country's state-owned broadcaster Television Tunisienne reported that Renard would arrive in Monterrey later on Tuesday to link up with the squad.
Renard, twice an Africa Cup of Nations winner, coached Saudi Arabia at the 2022 World Cup in Qatar and led them to a famous victory over eventual champions Argentina in the group stage.
He left to coach the French women's team at the World Cup in 2023 and the Paris Olympics, before returning to Saudi Arabia and helping the men's side qualify for a third successive World Cup.
He was then replaced by Georgios Donis in the build-up to the tournament.
FIFA World Cup 2026
The 2026 World Cup is taking place from June 11th to July 19th in the United States, Canada and Mexico. The tournament features 48 national teams and is played at 16 modern stadiums.
Match schedule and times | Group tables | How to watch the World Cup | World Cup Format | Past winners of the World Cup