A flame-holder device for an afterburner of a turbofan, the turbofan including a first inner annular casing and a second inner annular casing, these defining a passage for a primary flow, and an outer annular casing defining with the first inner annular casing a passage for a secondary flow, including at least one arm-support made of metallic material configured to be fixed to the outer casing by an upper plate and at least one flame-holder arm of a one-piece structure of composite material including two mutually attached walls arranged to define a groove whose profile is approximately a V. The walls support, on their upper part situated in the secondary flow, a fixing mechanism for fixing to the arm-support. The upper parts are approximately planar and are positioned facing each other.