He finished eighth (tied on points with seventh Junior Strous) in the European championship and eleventh in the French one, including a second place at Pau.

He continued in both series in 2006 with a fourth place overall in the Eurocup, including five podiums and a win at Le Mans, finishing just 11 points behind championship winner Filipe Albuquerque.

In 2007, Baguette entered the 3.5-litre Formula Renault 3.5 Series with the eponymous Kurt Mollekens-run KTR team, in which he took two podium finishes in his first season.

He continued in the category in 2008, driving for the Italian team Draco with which he scored his first win at Spa and ended seventh in the championship.

Baguette eventually won both races of the last meeting of the season at Ciudad del Motor de Aragón, thus winning the championship by 57 points from Fairuz Fauzy.

[1] On 22 March 2010, Conquest Racing announced that Baguette would drive their second car in the IndyCar Series, starting with the Indy Grand Prix of Alabama on 11 April.

During the race, he was constantly positioned within the first half of the field and on lap 189, manage a pass on Danica Patrick to take the lead of the 2011 Indianapolis 500.

[3] On the 6 Hours of Spa-Francorchamps, González, Baguette and Plowman finished in third position (for cars registered for points in the FIA World Endurance Championship), of LMP2 class (eleventh overall).

[4] In 2013 Baguette and his co-drivers Ricardo González and Martin Plowman from OAK Racing Morgan LMP2-Nissan team, won 81st edition of the 24 Hours of Le Mans in LMP2 class (seventh overall).

Their Morgan LMP2 covered a total of 329 laps in the Circuit de la Sarthe, the race was run in very difficult weather conditions and several serious accidents bringing out a record of twelve safety car caution periods.

17 Keihin Real Racing Honda NSX-GT equipped with Bridgestone tyres, partnering with Japanese driver Koudai Tsukakoshi.

After scoring the fastest overall time of the pre-season tests in Okayama in March,[19] the season was put on hold due to the coronavirus pandemic and Baguette returned to Belgium.

The pair were leading the championship on countback going into the final round at Fuji, where ten teams could potentially win the title.

They entered the final round with a chance to win the championship, eight points off the lead,[23] but early contact ended their race and they ultimately finished sixth in the standings.

[24] After eight years that saw him earn four victories, seven podiums and two pole positions, Baguette announced he would leave Honda at the end of the 2021 season.

[25] For the 2022 season, Baguette was signed by Nissan to drive for the famous Team Impul run by the legendary Kazuyoshi Hoshino.

[26] This move came after Nobuharu Matsushita made the exact opposite way around, taking the vacant seat left by Baguette on the n°17 Real Racing Honda.

During all season, the pair fought at the top of the field, scoring 4 podiums, with one of them being an incredible victory in the 5th round at Suzuka that saw Baguette and Hiramine starting deadlast on the grid, overtaking the n°17 Astema NSX for the lead with only 3 laps to go.

For the 2023 season, Nissan announced an unchanged lineup, with Baguette and Hiramine retained to defend their title, now driving the n°1 Calsonic Z.