The accurate characterisation of a copper–beryllium wire with a diameter of 0.1 mm is one of the steps to increase the precision of future accelerators' pre-alignment. Novelties in measuring the wire properties were found in order to overcome the difficulties brought by its small size. This paper focuses on an implementation of a chromatic-confocal sensor leading to a sub-micrometric uncertainty on the form measurements. Hence, this text reveals a high-accuracy metrology technique applicable to objects with small diameters: it details the methodology, describes a validation by comparison with a reference and specifies the uncertainty budget of this technique.