The formation process of fossil groups (FGs) is still under debate, and, due to the relative rarity of FGs, large samples of such objects are still missing. The aim of the present paper is to increase the sample of known FGs, and to analyse the properties of their brightest group galaxies (BGG) and compare them with a control sample of non-FG BGGs. Based on the large spectroscopic catalogue of haloes and galaxies publicly made available by Tinker, we extract a sample of 87 FG and 100 non-FG candidates. For all the objects with data available in UNIONS (initially the Canada France Imaging Survey, CFIS), in the u and r bands, and/or in an extra r-band processed to preserve all low surface brightness features (rLSB hereby), we made a 2D photometric fit of the BGG with GALFIT with one or two Sersic components. We also analysed how the subtraction of intracluster light contribution modifies the BGG properties. From the SDSS spectra available for the BGGs of 65 FGs and 82 non- FGs, we extracted the properties of their stellar populations with Firefly. To complement our study, we investigated the origin of the emission lines in a nearby FG, dominated by the NGC 4104 galaxy, to illustrate in detail the possible origin of emission lines in the FG BGGs, involving the presence or absence of an AGN. Morphologically, a single Sersic profile can fit most objects in the u band, while two Sersics are needed in the r and rLSB bands, both for FGs and non-FGs. Non-FG BGGs cover a larger range of Sersic index n. FG BGGs follow the Kormendy relation (mean surface brightness versus effective radius) previously derived for almost one thousand brightest cluster galaxies (BCGs) by Chu et al. (2022A&A...666A..54C) while non-FGs BGGs are in majority located below this relation, with fainter mean surface brightnesses. This suggests that FG BGGs have evolved similarly to BCGs, and non-FG BGGs have evolved differently from both FG BGGs and BCGs. All the above properties can be strongly modified by the subtraction of intracluster light contribution. Based on spectral fitting, the stellar populations of FG and non-FG BGGs do not differ significantly. The morphological properties and the Kormendy relation of FG and non-FG BGGs differ, suggesting they have had different formation histories. However, it is not possible to trace differences in their stellar populations or in their large scale distributions.