A framework structure (10) of a piece of home automation equipment on a wall (P), comprising an adjustable fastening system (S), including at least a support (1) and a holding device (M), the support (1) being able to be secured to the wall (P), the framework structure (10) comprising a chassis (10c) and at least two adjustable fasteners (6) each comprising a mechanical connection device (3) including an adjusting device (32) and a locking device (4), the framework structure (10) also comprising an attaching device (31) cooperating with the holding device (M) of the support (1), the adjusting device (32) allowing an adjustment of the chassis of the framework structure (10) along at least two directions that are orthogonal relative to the support (1).