Flörsch grew up near Munich, attending Oberhaching Grammar School before later basing herself in Pullach. She began karting in 2005 and by 2008 was competing across Europe through Kart Sport, becoming the first female and youngest driver in several karting championships including the 2008 SAKC Championship, the 2009 ADAC German Championship, and the 2010 European Championship Easykart. She was scouted by Red Bull during this period.
In 2015, Flörsch competed in the Ginetta Junior Championship for HHC Motorsport, winning twice and making double Ginetta history at Thruxton as the youngest driver to win a race and the first rookie to win two races in a single weekend. Financial difficulties curtailed her season midway through, at which point she was running third in the overall standings and leading the Rookie Championship.
She stepped up to the ADAC Formula 4 championship in 2016 with Motopark, becoming the first female driver to score points in the series on debut. In 2017 she achieved her first podium finishes at the Sachsenring and Hockenheim.
Flörsch joined Van Amersfoort Racing mid-season in the 2018 FIA Formula 3 European Championship, finishing 22nd overall. At the 2018 Macau Grand Prix, competing in the Formula 3 World Cup, she made contact with Jehan Daruvala on the fourth lap between Mandarin Corner and Lisboa Bend. The impact caused a front-left suspension failure that launched her car into the catch fencing at high speed before it smashed into a photographers' bunker. Flörsch was hospitalised along with Sho Tsuboi, two photographers, and a marshal. She was diagnosed with a spinal fracture and underwent surgery lasting almost ten hours, which was subsequently reported as successful with no risk of paralysis.
Her recovery was widely covered internationally and she was awarded the World Comeback of the Year prize at the 2020 Laureus World Sports Awards.
After the European F3 replacement series folded before a round was contested, Flörsch joined the Formula Regional European Championship for 2019 with Van Amersfoort Racing, scoring points in all 24 races and finishing seventh. She also competed at the 2019 Macau Grand Prix with the HWA Team but retired with a mechanical failure.
In 2020, Flörsch raced in the FIA Formula 3 Championship with Campos Racing, becoming the first woman to race in the series since its formation from the merger of GP3 and European F3. She finished 29th in the standings.
She returned to FIA Formula 3 in 2023 with PHM Racing by Charouz, having joined the Alpine Academy via the brand's new Rac(H)er programme. At Spa-Francorchamps, Flörsch took seventh place in a wet feature race, scoring six points and becoming the first female driver to score points in the FIA Formula 3 Championship — a historic milestone both for women in motorsport and for the Charouz squad, which had managed only a single point across the entire previous season.
From 2020, Flörsch combined her single-seater commitments with prototype racing. She raced for Signatech's all-female Richard Mille Racing Team in the European Le Mans Series and, notably, at the 2020 24 Hours of Le Mans, finishing ninth in LMP2 alongside Beitske Visser and Tatiana Calderón.
In 2021, she continued with Richard Mille in the FIA World Endurance Championship, qualifying a season-best sixth at the 8 Hours of Bahrain, ahead of Formula One race winner Juan Pablo Montoya. She also earned a call-up from Algarve Pro Racing for the ELMS season finale at Portimão, finishing third alongside Ferdinand Habsburg and Richard Bradley — the first woman to finish on an overall ELMS podium since Natacha Gachnang in 2013.
In 2022, she raced for Algarve Pro Racing in the ELMS, taking second place on debut at Paul Ricard alongside Bent Viscaal. She also entered the 24 Hours of Le Mans that year alongside Jack Aitken and John Falb, where a sensor issue at the start cost the trio five laps.
Alongside her 2021 FIA WEC programme, Flörsch raced in the Deutsche Tourenwagen Masters for Abt Sportsline with Schaeffler backing. As the only Audi running Schaeffler's experimental Space Drive steer-by-wire system, she had a difficult first half of the season before scoring eight points from the final six rounds in her GT3 debut year.
In December 2024, Flörsch signed with HMD Motorsports to compete in the 2025 Indy NXT series, but unexpected budget issues ended her campaign after a single race.
In 2026, she joined Opel's new Formula E works team as a test and development driver, marking her latest chapter in an evolving career across multiple categories.
Flörsch has been a consistent and public critic of gender-segregated motorsport series, describing the W Series as "a step back on a sporting level" and "not the way to help women in motorsport" at its 2019 launch. She has similarly criticised the F1 Academy as "segregation" and "the wrong approach."
She is a brand ambassador for the Schaeffler Group and supports the non-profit organisations Dare to be Different and Wings for Life. Her career is defined as much by her resilience — returning to race at Macau twice after her 2018 accident — as by her trailblazing results in formula racing.