Roy died last week at the age of 58 after a private three-and-a-half-year battle with pancreatic cancer, a diagnosis that remained undisclosed during his time in charge.
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Lachuer, a former Brest goalkeeper, had overseen the club's training sessions in recent weeks and holds the required coaching qualifications to lead a professional first team.
The 47-year-old, who has signed a two-year contract, will take charge ahead of the squad's return for pre-season training on 2 July.
Brest, however, continue to face uncertainty off the pitch after sporting director Gregory Lorenzi's departure to Marseille, while owner and president Denis Le Saint remains open to selling the club.