Francouz first played at the junior level within the ranks of hometown club, HC Plzeň. As a 15-year-old he backstopped the club's under-18 team in the 2005–06 season posting sub 2.00 GAA. In the following 2006–07 season he led the league with 25 wins. In the 2007–08 season, Francouz assumed the starting goaltender position at the highest junior level in the Czech Republic at the under-20 league. He recorded 25 wins in 37 games to lead the club into the post-season. Having signed a first team contract with HC Plzeň, Francouz made his professional debut in the Czech Extraliga during the 2008–09 season. In 15 games he collected 6 wins with a solid SV% of.922. At the under-20 level he finished the season with the League's best statistics in all categories. Francouz spent the next 2009–10 season continuing his development, appearing in 8 Extraliga games, while also playing in the Czech 1. Liga on loan to HC Tabor and SK Horácká Slavia Třebíč. On 13 May 2010, in order to earn more experience professionally, Francouz left Plzeň to sign a contract with HC Slovan Ústečtí Lvi of the Czech 1. Liga. In the 2010–11 season, he was initially loaned to former 1. Liga club SK Horácká before splitting the year in making an impact with his new club Ústečtí Lvi, posting the best GAA and SV% in the League and leading Slovan Ústečtí Lvi to the championship. During his second season with Ústečtí in 2011–12, Francouz strong play was rewarded as he was loaned and trained with HC Oceláři Třinec. He made in just one appearance with Třinec, allowing 4 goals against before he was replaced in the second intermission. On 9 May 2012, Francouz secured a place in the Extraliga agreeing to a contract with HC Litvínov beginning from the 2012–13 season. He instantly assumed Litvínov's starting role and in 46 games repaid the club by registering the most league wins with 26 and earn recognition as the Extraliga's Best Goaltender. In the 2014–15 season, Francouz through 46 games cemented his status as the best Goaltender in the Czech Republic, leading the league in most statistical categories, to earn the MVP award of both regular season and playoffs as Litvínov claimed the Championship.
After three years in Litvínov, Francouz opted to leave as a free agent and continue his career in Kontinental Hockey League by agreeing to a three-year contract with Russian outfit, Traktor Chelyabinsk on 30 April 2015. In his first season with Traktor in 2015–16, Francouz assumed backup duties to Vasili Demchenko. He posted a.924 save percentage despite collecting just 3 wins in 18 games as Chelyabinsk missed the post-season. In the following 2016–17 season, Francouz shared the starting role with Demchenko after initially earning KHL player of the week honors. He continued his strong play earning a selection to the 2017 All-Star Game. In 30 games with Traktor, Francouz accumulated 14 wins and finished the year with the KHL's best SVS%. Despite lucrative contract offers and interest, Francouz was not released from the final year of his contract and remained in Traktor for the 2017–18 season. He again shared starting duties and appeared in a season high 35 games for 15 wins and for the second consecutive season led the league in SVS%. Selected to backstop the club in the post-season, and led Traktor to the Conference Finals before suffering a series defeat to eventual Champions Ak Bars Kazan.
Colorado Avalanche
Francouz signed a one-year one-way deal of $690,000, contract with the Colorado Avalanche on 2 May 2018. On 1 July 2019 it was announced that Francouz would be the backup goalie for the upcoming season.
International play
Francouz was first introduced to the International stage at the Junior level, competing for Czech Republic at the Division I 2008 World U18 Championships in Kazan, Russia. As the team's backup he appeared in one game, helping Czech Republic place first in Group A and return to the Top Division for the following year. He next featured for the Czechs at the 2010 World Junior Championship. Francouz made his senior debut with the Czech Republic, competing in the 2013 World Championship. He made two relief appearances for the Czechs in a 7th-place finish. He was named to the roster of the 2014 World Championships, however failed to feature in a game before making his first full start at the 2016 World Championships. In the 2017 World Championships he shared netminding duties with Petr Mrázek, posting a 3–1 record with a 1.49 goals against and 9.10 save percentage. As an established member of the national team, Francouz was next selected to participate at the 2018 Winter Olympics in PyeongChang, Korea. As the first choice, Francouz appeared in every game for the Czech Republic, posting a 4–2 record in helping reach the semi-finals before losing to Russia. He was unable to prevent the Czechs suffer a 4–6 defeat in the bronze medal game against Canada on 24 February 2018. On 26 April 2018, Francouz was slated to make his fifth tournament appearance with Czech Republic after he was selected for the 2018 World Championships.
Personal
Francouz was born in Plzeň of then Czechoslovakia. When he first started playing hockey, Francouz was a defenseman. His first language is Czech, but he also gained English and Russian fluency in high school. He holds a pilot license, in which he uses throughout the off-season.