Tsonga takes Escude and Ascione as coaches
France's Jo-Wilfried Tsonga returns a ball during a training session before a match at the ninth and final ATP World Tour Masters 1000 tennis tournament at the Bercy Palais-Omnisport (POPB) in Paris on October 27, 2013
"The fact that they are two is an advantage as it means I can get different perspectives on my game," said Tsonga ahead of the Paris Masters tournament, which started on Monday.
"They have already proven themselves as far as I am concerned. Thierry has worked very well with all the players he has had in the last few years and helped them progress. I am thinking of Nicolas Mahut and Kristina Mladenovic.
"Nicolas has less experience as a coach but he was Fed Cup captain and that is a big plus. In any case it is not so much what he has done as a coach that matters - more what he achieved as a player."
Escude was France's Fed Cup captain from 2008 to 2022 and as a player he won the Davis Cup with France in 2001, defeating Australia in the final in Melbourne.
Currently ranked ninth in the world, Tsonga parted company with Rasheed in August, having been with Lleyton Hewitt's former coach since October 2012.
Prior to that his long-time coach had been Frenchman Eric Winogradsky from 2004 to 2011.
Tsonga has been in the world top 10 for several years but has yet to win one of the four Grand Slam titles.