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Juniors

Van Assche won the 2021 French Open Boys' Singles title, defeating fellow countryman Arthur Fils in the final.

2022: ATP, Major doubles debuts, Maiden Challenger title and top 150

In January 2024, ranked No. 445, Van Assche received a wildcard for the qualifying event at the 2022 Open Sud de France but lost to Roman Safiullin. He also made his ATP main draw doubles debut after receiving a wildcard into the main draw with Sascha Gueymard Wayenburg where they defeated David Vega Hernandez and Denys Molchanov to win their first ATP tour level match. He also made his Grand Slam debut in doubles at the French Open as a wildcard pair partnering also Gueymard Wayenburg.

In October, Van Assche reached his first singles final on the ATP Challenger Tour in Lisbon, Portugal, entering the main draw as a qualifier and losing to Marco Cecchinato in the finals. As a result he broke into the top 250. The following week, he made his ATP singles debut in Antwerp after qualifying for the main draw.

On 14 November 2022, he entered the top 200 at world No. 198, after reaching the final of the Brest Challenger losing to Gregoire Barrere and the quarterfinals in Roanne. In December, Van Assche won his maiden Challenger title in Maia defeating qualifier Maximilian Neuchrist in the final. As a result he moved to No. 138 in the rankings, making him the youngest player in the top 150.

2023: Major and Masters debuts, Two Challengers 125 titles & top 100, first ATP win

Van Assche received a wildcard into the 2023 Australian Open main draw to make his Grand Slam debut in singles.

He then competed in the Teréga Open Pau–Pyrénées Challenger 125 (indoor), defeating Ugo Humbert in the final in 3 hours and 56 minutes, which set a record for the longest ATP Challenger final and saving two match points. Following his second title win in Pau, he moved close to 40 positions up and reached the top 110 on 6 March 2023. Following his title at the 2023 Sanremo Challenger 125 (clay) he reached No. 91 on 3 April 2023 making him the youngest player in the top 100. The following week he recorded his first ATP win at the 2023 Estoril Open over qualifier Pedro Sousa after entering into the main draw directly. He recorded his first top-100 win over Stan Wawrinka at the 2023 Srpska Open.

Van Assche recorded his first Grand Slam win at the 2023 French Open defeating Marco Cecchinato in the first round before losing to Alejandro Davidovich Fokina in the second round. He made his Wimbledon debut in July, losing to Aslan Karatsev in the first round. At Wimbledon, Van Assche recorded his first Grand Slam doubles win, playing along with fellow countryman Arthur Fils, defeating brothers Stefanos Tsitsipas and Petros Tsitsipas in the first round.

In November, he qualified for the 2023 Next Generation ATP Finals.

2024: Australian Open debut and third round

At the 2024 Australian Open he reached the third round defeating James Duckworth and 25th seed Lorenzo Musetti on his debut at this Major.