Louis Moutin was born in Paris on December 24, 1961, into a family whose record collection gave him an early passion for jazz. He taught himself piano at seven, then switched to drums at twenty. In between he completed an engineering degree at the École Centrale de Lyon and a master's degree in mathematics, finishing both in 1985 at age twenty-four, before deciding to set the technical career aside and become a professional jazz musician.

Within a few years he was working with pianist Jean-Marie Machado's Trio Machado, documented on 1993's Séquence Thmiryque (Label Bleu), and had built a reputation as one of the strongest drummers on the European scene. At twenty-nine he teamed for the first time with his twin brother, double bassist François Moutin, to record Parcours (1991, Blue Line Productions) as the Louis Et François Moutin Quintet, alongside saxophonists Simon Spang-Hanssen and Sylvain Beuf and flutist Marianne Spang-Hanssen.

In 1998 the twins founded the Moutin Reunion Quartet, sustaining the group across the Atlantic even after François relocated to New York the previous year. Power Tree (2000, Shaï; reissued 2001 on Dreyfus Records and 2004 on Nocturne) introduced the band with pianist Baptiste Trotignon and saxophonist Sylvain Beuf. Tenor saxophonist Rick Margitza joined for Red Moon (2003, Nocturne) and stayed through Something Like Now (2005) and the CD/DVD set Sharp Turns (2007), both with pianist Pierre de Bethmann, and Soul Dancers (2009, Plus Loin Music). Across five studio albums and, by the group's own account, more than 450 concerts, the Moutin Reunion Quartet built its identity on original material written separately by each brother and performed with the interplay of a band that had spent a lifetime finishing each other's musical sentences.

The brothers launched a second group, the Moutin Factory Quintet, in 2013, debuting at the Jazz in Marciac festival with guitarist Manu Codjia, alto and sopranino saxophonist Christophe Monniot, and pianist Thomas Enhco on Lucky People (2013, Plus Loin Music). Pianist Jean-Michel Pilc took the piano chair for Deep (2016, Jazz Family), and Paul Lay held it for Mythical River (2019, Laborie Jazz), recorded in Paris immediately after the quintet returned from a two-week tour tracing the Mississippi River. Three of that album's tracks were originally written for No Human Is Illegal, Richard Ledes's 2017 documentary about refugees detained on the Greek island of Lesvos. Later dates continued the pattern of pairing the twins with a rotating third or fourth voice: M.O.M. (2021, Laborie Jazz) with reedman Jowee Omicil, and Lake of Dreams (2023) with pianist Arkadiy Figlin.

Alongside his own bands, Louis built one of the busiest sideman careers in French jazz. He recorded with pianists Antoine Hervé (Invention Is You, 2001, Enja), Giovanni Mirabassi (Architectures, 1999; Prima O Poi, 2005, alongside trumpeter Flavio Boltro), Manuel Rocheman, and Christophe Laborde (Wings of Waves, 2013, Cristal Records); with pianist Martial Solal's trio on Longitude (2008, CAM Jazz); with bassist and composer Henri Texier's Hope Quartet and Sky Dancers ensembles (At l'Improviste, 2013; Sky Dancers, 2016, both Label Bleu); and with pianist Tigran Hamasyan's trio on New Era (2007, Plus Loin Music). In 2013 he drummed on the entirety of Israeli saxophonist Shauli Einav's Paris-recorded, all-original album A Truth About Me (Cristal Records), a session that also featured saxophonist and clarinetist Antonin-Tri Hoang and pianist Paul Lay. In 2005 the Académie du Jazz awarded its Prix Django Reinhardt, honoring the year's outstanding French jazz musician, jointly to Louis and François Moutin.

Moutin's playing sits inside hard bop and post-bop's harmonic and rhythmic language while reaching past it: reviewing the Moutin Reunion Quartet's Something Like Now, All About Jazz's Chris May wrote that the brothers' largely acoustic music "borrows as much, philosophically if not sonically, from fusion groups like Weather Report as it does classic influences like John Coltrane and Charlie Parker." That dual inheritance shows up literally in performance: the quartet's concerts and records have featured spontaneous medleys built from Coltrane and Parker themes, and the Moutin Factory Quintet's Mythical River closes one piece with a similar tribute to Wayne Shorter. Reviewing that record, All About Jazz's Dan Bilawsky called the results "bold, bracing, and thought-provoking," ranging from Middle Eastern-tinged mystery to blues-drenched swing across a set partly composed for a documentary about refugees. Whichever band is on the bandstand, Moutin and his twin brother function as a single rhythmic unit first and soloists second, an interlock reviewers have repeatedly singled out as the two groups' defining trait.