Dillmann began motorsport in karting from 2000 to 2002, winning a regional title in France. He entered the Formula Renault 1600 Belgium series in 2004 with his family-run Tom Team, finishing fifth and claiming a victory at Spa-Francorchamps. Moving into the Formula Renault Eurocup in 2005 with Prema Powerteam alongside Kamui Kobayashi, he struggled early and stepped back, before returning in 2006 with SG Formula and claiming his first Eurocup podium at Misano.
Dillmann joined the Red Bull Junior Team ahead of the 2007 Formula 3 Euro Series season, racing for ASM alongside Romain Grosjean, Nico Hulkenberg, and Kamui Kobayashi. A pre-season crash that broke his sternum and a vertebra caused him to miss the opening round, but he finished ninth overall with three podiums. He remained in the category through 2009 before committing full-time to the German Formula Three Championship in 2010 with HS Technik, winning the title and becoming the first French driver to claim the German Formula Three championship. Key victories came at the Sachsenring, Hockenheim, and Nurburgring; he ultimately edged Daniel Abt by a margin secured when Abt's car suffered a broken lambda sensor at Oschersleben in the final round.
In 2011, Dillmann competed in the GP3 Series with Carlin, qualifying on pole at the season opener in Istanbul, before moving to Addax Team mid-season and finishing fourteenth in the standings. He moved up to GP2 for 2012 with Rapax, taking his first win in the Bahrain sprint race. Further campaigns with Russian Time in 2013 — where he scored two pole positions alongside GP2 returnee Sam Bird — and with Arden International and Caterham in 2014 followed, the latter disrupted by the death of the Russian Time team principal.
In 2015, Dillmann contested the Formula V8 3.5 Series with Jagonya Ayam with Carlin, finishing seventh. The following season he switched to AVF, winning two races, securing five pole positions, and claiming the championship by seven points over Louis Deletraz at the final round. In Formula E, Dillmann made a full-season appearance with Nio in 2018-19, finishing twenty-third in the standings, and since May 2021 has served as simulator and reserve driver for Jaguar Racing.
Dillmann entered World Endurance Championship competition in 2015 with Signatech Alpine, winning his debut race at the 6 Hours of Shanghai. He drove for ByKolles Racing in the LMP1 class across the 2018-19 and 2019-20 WEC seasons, managing a best result of fourth despite the team's reliability difficulties. In 2023 he joined the Vanwall Racing Team alongside Esteban Guerrieri and Jacques Villeneuve in the Le Mans Hypercar class, departing in June 2023 citing a desire to pursue other opportunities.
In the Le Mans Cup, Dillmann claimed the overall 2022 championship with Racing Spirit of Leman alongside Alexander Mattschull, winning three races during the season.
In four earlier Le Mans starts between 2018 and 2023, Dillmann did not finish. His fortunes changed dramatically in 2025 when, driving for Inter Europol Competition in the LMP2 class alongside Jakub Smiechowski and Nick Yelloly, the trio won the race outright in their class. The number 43 car led through the final morning and survived a dramatic last-hour drive-through penalty for speeding in pit lane, regaining the lead when a suspension failure struck the Panis Racing rival car. Dillmann successfully defended the victory in 2026 with the same teammates, being credited as the fastest driver of the crew and spending more than ten hours in the car.
Dillmann joined Inter Europol Competition in the IMSA SportsCar Championship from 2024, partnering Nick Boulle and Smiechowski. He won the IMSA LMP2 title in his debut IMSA season, secured by a victory at Canadian Tire Motorsport Park and consistent podium results. In the European Le Mans Series, he finished second overall in 2024 and again in 2025, earning the Goodyear Golden Wingfoot Award in 2025 as the series' fastest driver by average stint time. He also competed in the Asian Le Mans Series from 2023-24, achieving a best overall finish of third in the 2025-26 season with Algarve Pro Racing.
Dillmann married Nicolle in 2018 and the couple have a daughter born in 2021.