Baptiste Trotignon was born June 17, 1974, in Meulan-en-Yvelines, in the Yvelines department west of Paris. He took up the violin at six and switched to piano at nine, following his amateur-pianist father's example, and joined the regional conservatory in Nantes, where he won prizes in both piano performance and composition while teaching himself jazz by ear. As a teenager he had a small acting turn as a young jazz pianist in Alain Corneau's 1995 film Le Nouveau Monde. He then moved to Paris and entered the jazz program at the Conservatoire National Supérieur de Musique. In 1996 he placed second soloist at the Concours National de Jazz de la Défense and was named a "new talent" by the magazine Jazzman.

Trotignon formed his first trio in 1998 with bassist Clovis Nicolas and drummer Tony Rabeson, and their debut album Fluide (2000, Naïve) won the Django d'Or for best first record. A second trio album, Sightseeing, followed in 2001. In October 2002 he won the Grand Prix de la Ville de Paris at the Martial Solal international jazz piano competition, and a few months later took the Révélation Instrumentale Française prize (the Prix Frank-Ténot) at the 2003 Victoires du Jazz. That same year he released Solo, his first unaccompanied piano record, followed by Solo II in 2005 (reissued in 2008 with a solo concert recorded at the Salle Pleyel). Through the mid-2000s he also co-led a quartet with tenor saxophonist David El-Malek, bassist Darryl Hall, and drummer Dré Pallemaerts, cutting a self-titled studio album in 2005 and the double live set Fool Time in 2007, and led the trio date Flower Power (2006) with drummer Aldo Romano and bassist Rémi Vignolo.

From the late 2000s Trotignon built a parallel body of work with New York-based musicians. Share (2008, recorded in New York with bassist Matt Penman and drummers Otis Brown III and Eric Harland, with guest turns from tenor saxophonist Mark Turner and flugelhornist Tom Harrell) was followed by Suite... (2009), a live London quartet recording with Turner, trumpeter Jeremy Pelt, Penman, and Harland. He returned to the duo format with Turner alone on Dusk Is a Quiet Place (2013) and to a trio, with bassist Thomas Bramerie and drummer Jeff Ballard, on Hit (2014).

Alongside his jazz output, Trotignon developed a substantial second career as a composer for the concert hall. His piano concerto Different Spaces, dedicated to and premiered by pianist Nicholas Angelich with the Orchestre National Bordeaux Aquitaine under Paul Daniel in November 2012, was recorded and released in 2015; it won the Grand Prix Lycéen des Compositeurs from the Maison de la Musique Contemporaine in 2017. He later composed Anima (2022) for the Orchestre Victor Hugo Franche-Comté under Jean-François Verdier, and worked as pianist-arranger on a run of classical and art-song projects, including Thousands of Miles (2017), a duo recital with mezzo-soprano Kate Lindsey, and Because (2023), a program of spirituals and songs by Florence Price recorded with countertenor Reginald Mobley.

Trotignon signed to Sony's Okeh imprint in the mid-2010s, releasing the duo record Chimichurri (2016) with percussionist Minino Garay and the quartet album Ancestral Memories (2017), co-led with saxophonist Yosvany Terry, bassist Yunior Terry, and drummer Jeff "Tain" Watts. His 2019 album You've Changed paired his own solo piano playing and compositions with a different guest voice or horn on each of several tracks, among them saxophonist Joe Lovano, trumpeter Avishai Cohen (Trumpet) on the title track, trumpeter Ibrahim Maalouf, singer Camélia Jordana, singer Thomas de Pourquery, and cellist Vincent Segal. He returned to trio playing on Brexit Music (2023), a set of British pop and rock repertoire from the Beatles to Radiohead recorded with Penman and drummer Gregory Hutchinson, and in 2024 released PianoForte, a four-piano collaboration with fellow French pianists Eric Legnini, Pierre de Bethmann, and Bojan Z, and Piano Voix, a duo record with singer Arthur Teboul. PianoForte won Best Album and Best Concert at the 2025 Victoires du Jazz.

Critics have consistently singled out Trotignon's technical range rather than any single stylistic lineage. Writing in The Daily Telegraph in 2009, Ivan Hewett described Trotignon's playing as distinctly his own, marked by rapid unison-note repetitions and fast hand-to-hand alternations that function as personal signatures rather than borrowed devices. The Guardian's John Fordham, reviewing a duo performance with percussionist Minino Garay, noted the way Trotignon's playing moves between startling chordal outbursts, a plaintive lyrical side, and sharper, more percussive lines. That range shows up across his catalog: he has worked as a trio and quartet leader in a straight-ahead post-bop idiom, as a duo partner to saxophonists and singers, as a soloist reinterpreting repertoire from Bach to Led Zeppelin, and as a composer of orchestral and chamber works, without treating any one of those lanes as a detour from the others.