Youth Souquet was born in Paris and began his career playing for CO Vincennois, the same club that produced the likes of
Blaise Matuidi and
Yacine Brahimi. While attending the
Vincennes-based club, Souquet had the opportunity to join both the famous
Clairefontaine academy and the Parisian giants
Paris Saint-Germain. However, he declined the chance and after his father met with then-president
Alain Cayzac of the latter, he declined that chance, as well.
Lille Souquet joined
Lille in 2007 as a youth player after the club spotted him while playing with Vincennes. After excelling in the club's youth system and internationally, for the
2008–09 season, he was promoted to the club's
Championnat de France amateur team, despite being only 16 years old at the time. He made his debut with the reserves in their 1–5 defeat to
AS Nancy reserves on 14 September 2008. Over the course of the season, he made 12 appearances, which included nine starts. Following the season, on 17 July 2009, Souquet signed his first professional contract agreeing to a three-year deal. After starting the season with the club's
Championnat de France amateur team, on 30 September 2009, due to injuries to midfielders
Florent Balmont and
Ludovic Obraniak, manager
Rudi Garcia announced that Souquet would be included in the team for the club's match against
Czech club
Slavia Prague in the
UEFA Europa League. Souquet was assigned the number 35 shirt and made his professional debut, as a starter, playing the entire 90 minutes. In the match, which Lille won 5–1, Souquet scored his first professional goal in the 88th minute and also assisted on a goal scored by
Pierre-Alain Frau. On 17 October, he made his league debut starting in the club's match against
Rennes. The match ended 0–0 with Souquet only playing the first half.
Nice On 25 July 2016,
Ligue 1 side
Nice reached an agreement with
Dijon for the transfer of Souquet.
Gent On 31 August 2018, the last day of the 2018 summer transfer window, Souquet joined
Belgian First Division A side
K.A.A. Gent on a four-year contract. The transfer fee was reported as €3 million.
Montpellier On 6 August 2019, Souquet joined
Montpellier HSC.
Chicago Fire On 9 January 2023, Souquet moved to
Major League Soccer side
Chicago Fire on a 3-year deal. On 13 February 2025, Souquet was released by Chicago Fire. ==International career==