Giltaire began competitive karting in 2018, finishing seventh in the French Championship in his class and eleventh in the Rotax Max Challenge Grand Finals. His breakthrough in karting came in 2022, when he won both the SKUSA SuperNationals XXV and the IAME Warriors Final in the X30 Senior category. He also reached fourth in the IAME Euro Series and fifth in the CIK-FIA Karting European Championship that year. In 2023 he combined his single-seater debut campaign with continued karting, finishing third in the IAME Winter Cup.
He was a finalist in the 2022 Richard Mille Young Talent Academy shootout, a programme designed to identify promising junior talent.
Giltaire made his single-seater debut in the 2023 French F4 Championship. He entered an immediate title fight with compatriot Enzo Peugeot and Canadian Kevin Foster, collecting six wins, eight pole positions, and thirteen podiums across the season. He secured the championship at the final round at Circuit Paul Ricard, edging Peugeot by four points.
Following his French F4 title, Giltaire was invited to compete as a guest driver in the final two rounds of the 2023 Formula Regional European Championship with ART Grand Prix. His best result was eleventh place at Circuit Zandvoort; as a guest entry he was ineligible for championship points and finished third among guest drivers.
Giltaire graduated to a full-time seat in the 2024 Formula Regional European Championship with ART Grand Prix. He retired from the opening race at the Hockenheimring but won the second race to claim his maiden Formula Regional victory. His season was otherwise inconsistent, with a second podium at the Red Bull Ring and a points finish at Monza in the penultimate round. He finished seventh in the drivers' championship with 97 points.
He also contested the 2024 Macau Grand Prix with ART, qualifying ninth, finishing ninth in the qualifying race, and retiring from the main race following a first-lap accident.
Giltaire remained with ART Grand Prix for 2025, competing in both the Formula Regional Middle East Championship and the Formula Regional European Championship. In the Middle East series he clinched the title during the second race at the Lusail International Circuit, having fought a close battle with Freddie Slater throughout the campaign. He accumulated three wins, five pole positions, two fastest laps, eight podiums, and 264 points.
His sophomore FRECA campaign brought a fifth-place championship finish; Giltaire described the season as frustrating and signalled his intention to move to Japan.
In March 2026, Giltaire confirmed a move to the 2026 Super Formula Lights season with B-Max Racing Team, continuing a career trajectory that has taken him from French karting to Japan's premier junior single-seater series within three years of his racing debut.
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