Until at least 1631 Denis's career was closely linked to that of his older cousin, Ennemond; so much that contemporary writers referred to either composer by surname only, making no attempt to distinguish between them.
Both lutenists had connections with Blancrocher and Henri de L'Enclos, and both secured a high reputation comparable to that of François Dufaut, Jacques Gallot, or Charles Mouton.
In general, Gaultier was a masterful melodist, effortlessly writing graceful melodic lines with clear phrase structures, but his music is less inventive harmonically than that of some other French lutenists of the era, such as René Mesangeau or Pierre Dubut.
Nevertheless, Gaultier was an important exponent of the French style brisé, and as such an influence on harpsichordists such as Johann Jakob Froberger.
Around 1680 a few of Gaultier's works were included in anthologies by Perrine, a French theorist who experimented with the writing of lute music in staff notation.