Born in Cannes, Boccolacci began karting in 2007 at the age of nine, competing in competitions across Europe. He graduated to single-seaters in 2014, competing in the French F4 Championship. There he scored two victories, pole positions and fastest laps and finished as Junior champion and runner-up in the overall standings. In 2015, Boccolacci switched to the FIA Formula 3 European Championship, racing with Signature. In contrast to his season in French F4, Boccolacci only finished twelfth in the rookie championship and nineteenth in the overall standings. He subsequently stepped down on the ladder, joining Tech 1 Racing for the 2016season of the Formula Renault Eurocup and NEC series.[2] Scoring three wins across both series, Boccolacci finished runner-up in the Eurocup standings and third overall in NEC.
In November 2016, the Frenchman made his GP3 debut in the post-season test at Yas Marina with Arden International and DAMS.[3][4] He would eventually join Trident for the 2017 season.[5] During the campaign, Boccolacci achieved a race win at the final round, which helped him towards sixth place in the championship.[6] He returned for the following season, switching to newcomers MP Motorsport.[7] Once again, the season yielded one win, though another win went begging when he was stripped from victory post-race at Le Castellet due to a technical infringement. Boccolacci ended up tenth in the standings, switching to Formula 2 in the middle of the year to replace Roberto Merhi at MP, where he scored two points finishes. In 2019, the French driver began the F2 season at Campos Racing alongside Jack Aitken.[8] Having struggled at the opening round, stronger performances at the street circuits of Baku and Monaco gave Boccolacci his first points of the year.[9] However, Boccolacci left the team after the next round, only returning for a one-off appearance at Silverstone for Trident.[10][11][12]
During his pathway up the single-seater ladder, Boccolacci was also named as one of the eight drivers to be signed to the Venturi Formula E team's new Next Gen Programme in 2018.[13]
For 2021, Boccolacci switched to the Porsche Carrera Cup world, driving full campaigns in the main Supercup series as well as the Porsche Carrera Cup France with Martinet by Alméras. He scored two podiums in the former, which included third place at the Monaco Grand Prix support race — Boccolacci's debut in the series — on his way to sixth place overall. The latter championship yielded even more success, as Boccolacci won four races, including both races at the first round, and came close to the title, losing out to Marvin Klein by just three points at the final round.[19][20] Said event decided the title in spectacular fashion, with Boccolacci colliding with his title rival, therefore handing the championship to Klein.[21]
Boccolacci remained at Alméras for both the Supercup and PCCF seasons in 2022. He improved his finishing position at Monaco with a second place, but would ultimately end up seventh in the Supercup standings, as two retirements blighted his campaign.[22] Meanwhile in the French championship, Boccolacci took five victories and finished on the rostrum in all but two races on his way to another runner-up finish to an ultimately dominant Marvin King.[23][24] For his third year racing Porsches, Boccolacci made a switch to CLRT. This would end up being his most successful Supercup season to date, as he scored his first pole position at Silverstone and took two podiums, which contributed to him placing fifth overall.[25][26] His third PCCF season meanwhile finally brought him the title, which Boccolacci attained after pairing a win at Magny-Cours with five successive victories in the final five races, allowing him to beat Alessandro Ghiretti by 24 points.[27][28]