Jean-Jacques "Babik" Reinhardt was born in Paris on June 8, 1944, the younger son of Django Reinhardt and Naguine. His elder half-brother Lousson also played guitar, but the two grew up in different households and rarely met. Django died in 1953, when Babik was nine, and the boy learned the instrument not from his father but from relatives and contemporaries: his uncles Joseph "Nin-Nin" Reinhardt and Eugène Vées, and Vées's sons Loulou and Mitsou. According to the writer Fred Sharp, Django had steered him toward the piano, reasoning that a pianist would find more work than a guitarist. At fifteen Babik appeared in Jean-Christophe Averty's 1959 film Hommage à Django Reinhardt, playing rhythm guitar behind Vées, Joseph Reinhardt and Stéphane Grappelli.

His first professional steps were in rock and roll. By eighteen he was playing electric guitar with Glenn Jack et ses Glenners, a French group led by Jacques Vérières, and he appears on their 1962 EPs for Disques Festival. He returned to jazz in the mid-1960s, working the Paris clubs and, according to French Wikipedia, sharing the stage at Les Trois Mailletz with Jean-Luc Ponty for several months. His first jazz recordings came in 1967 for Disques Vogue with the organist Georges Arvanitas: the four-track EP Swing 67, which paired two of his originals with two of his father's, and an album of Sidney Bechet tunes, Joue Sidney Bechet, on which he played a Gibson electric guitar.

His own albums followed through the 1970s: Sinti Houn Brazil (CBS, 1973), which leaned toward bossa nova, and Sur le chemin de mon père...Django (Music For Pleasure), a program of his father's compositions played in a mainstream electric style. French Wikipedia says he made many concerts between 1967 and 1973, including a six-month tour of the United States, and then took a pause from his career. In the 1980s he played on Stéphane Grappelli's Anniversary Concert and toured with the violinist Didier Lockwood, Larry Coryell and Béréli Lagrène. Three of a Kind (JMS, 1985) paired him with the guitarists Christian Escoudé and Boulou Ferré in a contemporary setting that closed with a tribute to Django.

From 1988 he recorded mostly for the French label RDC Records, with Franck Hagege as producer: All Love (1988), Nuances (1992, with guests including Grappelli, Lockwood and the percussionist and drummer Aldo Romano), and Vibration (1995), all in a mainstream and contemporary jazz style. In 1992 he co-founded, with Jacqueline Danno and Hagege, the association Arts, Nuances, Cultures, which runs the Djangodor awards honoring established musicians and new talent. He wrote and arranged music for two French films, Le Prix du silence (1990, directed by Jacques Ertaud) and Mohammad Bertrand Duval (1991, directed by Alex Métayer).

In his last years he worked on both sides of the Atlantic. He recorded A Night in Conover live in North Carolina in September 1997 with the guitarist François Vola, the bassist Zach Page and the violinist and mandolinist Emory Lester; made New Quintette du Hot Club de France (1998) with the guitarist Romane, a lightly swinging, modernized take on the original Hot Club sound; and recorded Django d'Or at OAL Studios on November 19 and 20, 1998 with the clarinetist Putte Wickman and the guitarist Ulf Wakenius. His last New York appearance was at Birdland in 2000. He died of a heart attack in Cannes on November 13, 2001, at the age of 57. His son David Reinhardt, born in 1986, is also a guitarist, and a track by Babik appeared on the 2009 tribute album Generation Django (Dreyfus), alongside David and Béréli Lagrène.

Reinhardt was the son of the most famous guitarist in European jazz, and the career he built was not a copy of it. He learned the Sinti guitar tradition at first hand from his uncles, and he returned to his father's repertoire throughout his life, but his own voice was an amplified one: a Gibson electric guitar, bossa nova and Brazilian rhythms, and the harmonic language of postwar American jazz. French Wikipedia names Jimmy Raney, Wes Montgomery, Tal Farlow and John Coltrane among the players he admired, and his own track titles such as "Cool Trane" and "Coltrane Memory" point the same way. English Wikipedia describes him as drawn more to fusion than to Gypsy jazz, and he recorded with Larry Coryell and Didier Lockwood, both fusion-minded players. His albums sit mostly in the mainstream and contemporary jazz idiom, with the Django material (the 1998 Hot Club quintet record above all) as the strand that links him back to his family's music.