Foulquier was awarded the Best Academy Player award for the 2009–10 season.[3] After appearing on the bench in matches during the 2010–11 season,[4] he was promoted to the senior team by manager Frédéric Antonetti for the 2011–12 season. He was assigned the number 24 shirt and made his professional debut on 2 October 2011 in a league match against Lille, starting but being replaced at half-time in a 2–0 away loss.[6] He made 22 total appearances, including his UEFA Europa League debut in a 3–1 loss at Atlético Madrid on 15 December,[7] and was sent off on 11 May 2013 in a 4–1 loss at Valenciennes for two yellow cards in the space of three minutes.[8]
On 25 May 2014, the Andalusians bought Foulquier outright, for a €2 million fee, with the player signing a five-year deal.[11] He scored the only goal of his spell on 24 October 2015, in the third minute of a 1–1 draw with Real Betis at the Nuevo Estadio de Los Cármenes.[12]
Watford
Foulquier signed for Watford on 25 August 2017, with the club also being owned by the Pozzo family.[13] He was immediately loaned back to his birth country's top league, joining Strasbourg for the season.[14] The early part of his spell was affected by injury.[15]
On 23 August 2018, Foulquier returned to Spain and its first division after agreeing to a one-year loan deal with Getafe.[16] He played 25 times in a 5th-place season that secured Europa League qualification, scoring in consecutive wins at Rayo Vallecano and at home to Betis in October.[17][18]
Foulquier made his Watford debut on 27 August 2019 in the second round of the EFL Cup, a 3–0 home win over Coventry City.[19] On 21 September he made his Premier League bow, being replaced by Roberto Pereyra after 33 minutes of an 8–0 loss at reigning champions Manchester City; it was 5–0 after 18 minutes.[20]
Granada return
On 2 January 2020, Foulquier returned to Granada on loan for the rest of the season with the option to buy.[21] He played regularly as the campaign ended in 7th place and European qualification, and scored in a 3–0 win at Osasuna on 23 February.[22] His move was made permanent through a buying option on 24 July, signing him to a three-year contract.[23]
Valencia
On 30 August 2021, Foulquier signed a four-year deal with Valencia, also in the top tier, for a fee of €2.5 million.[24] He made seven appearances as they finished runners-up in the Copa del Rey, being substituted for Yunus Musah in the 100th minute of the final 1–1 draw with Betis in which his replacement was the only one to miss in the penalty shootout.[25]