Meslier began playing football with his local club Merlevenez at the age of 6, and after a successful match against FC Lorient joined their academy. On 1 February 2018, he signed his first professional contract with Lorient. In July 2018, Lorient rejected a €10 million bid from Ligue 1 side AS Monaco for Meslier. he also received interest from English Premier League side Chelsea. He stayed at Lorient, and shortly made his professional debut under then Manager Mickaël Landreau for Lorient in a 1–0 Coupe de la Ligue win over Valenciennes FC on 14 August 2018. He kept a clean sheet consecutively in his first 5 games as a professional, conceding his first ever goal in his 6th game against Paris FC. He saved an injury time penalty from Clermont player Manuel Perez in Lorient's 1-0 win against Clermont. He solidified his place as the clubs number 1 season during the 2018/19 season, playing 30 times in all competitions, keeping 11 clean sheets. With his form helping Lorient finish in 6th in 2018–19 Ligue 2 but narrowly missing out on the playoffs due to goal difference compared with RC Lens.
Leeds United (loan)
On 8 August 2019, Meslier was signed on a season-long loan by English Championship team Leeds United, with Leeds also having the option to buy Meslier on a permanent deal. He started the season as second choice goalkeeper behind Kiko Casilla and competing with Kamil Miazek for a place on the bench, Meslier gained a reputation as a penalty saving expert after saving three separate penalties for Leeds United under-23's by December. On 4 January 2020, head coachMarcelo Bielsa announced that Meslier would make his debut on 6 January in Leeds' FA Cup tie against Premier League side Arsenal. With Meslier putting in an impressive performance against the Premier League side in a 1–0 defeat on his debut, he was praised for his distribution and his saves during the match. On 29 February 2020, he made his league debut for Leeds in a 4–0 victory away at Hull City.
Leeds United
On 23 July 2020, Meslier joined Leeds permanantly following their promotion to the Premier League, signing a 3-year contract.
International career
Meslier has been capped at international level by France, all the way up to France U20's. He was also part of the France U20's squad for the FIFA U-20 World Cup during the 2019 FIFA U-20 World Cup playing as the 1st choice goalkeeper in May 2019. In November 2019, Meslier was called up the France U21's squad and was named as an unused substitute in a 3-1 defeat against Switzerland U21's on 19 November 2019.
Style of play
Due to his appearance and physical stature, Meslier's goalkeeping style has been compared to that of Belgian goalkeeper Thibaut Courtois.
