Baup signed on as the manager of Saint-Étienne in 2004, bringing to the club one of his favourite players, Pascal Feindouno. Saint-Étienne had won promotion to Ligue 1 at the end of the 2003-2004 season. During Baup's tenure, the club finished sixth and thirteenth in the table respectively in the 2004-05 Ligue 1 and 2005-06 Ligue 1 seasons. He resigned from the club at the end of the 2005-2006 season.
Baup became the manager of Ligue 1 club Nantes on 28 August 2008. He resigned from the club on 2 June 2009, with over a year to run on his contract, after he had failed to save it from relegation to Ligue 2. 
In the afternoon of 7 December 2013, the club announced on its website that Baup was no longer the Olympqiue de Marseille manager. The club president (Vincent Labrune) and Baup had earlier held a meeting right after the end of the training session conducted in the morning of 7 December 2013. "The board feel that, after 17 league matches into the season, results have not corresponded with our objectives and a firm decision had to be taken to get the team moving in the right direction again in the coming weeks," read a statement on the club's official website. Vincent Labrune said that the decision to dismiss Baup was "the most difficult and painful he had had to take since he came to the club". "Elie Baup is unanimously appreciated for his qualities as a person," Labrune added. "Nobody can forget the job he has done at Olympique de Marseille. He enabled us to finish second last season when nobody expected us to." The decision to sack Baup came just a day after Marseille went down 1-0 to Nantes at the Stade Velodrome in a Ligue 1 match that left them in 5th position and 13 points behind leaders Paris Saint-Germain in the Ligue 1 table at the conclusion of the week 17 matches. Marseille had also fared poorly in the 2013-14 UEFA Champions League. They had so far failed to pick up a single point from their first five Group F matches against Arsenal, Borussia Dortmund and Napoli, thus ensuring that they would finish at the bottom of the group. 
^Baup played for the Toulouse youth team in 1970–1974. He also played for US Larroque (1966–1970), SO Mazamet (1974–1978) and Muret (1978–1981), but there is no information about appearances and goals.