For electrical work, the business must hold an RBQ contractor licence that includes the right subcategory (16). Here is which one, and where to find businesses that hold it.
RBQ subcategory (official title, in French): 16.0 Entrepreneur en électricité.
The business's qualifications and solvency were checked before its licence was issued. Under certain conditions, its bond may also compensate you for a lost deposit, unfinished work or defects found within a year of completion.
Official sources: Building Act, s. 46 · Building Act, s. 7 · Regulation respecting the professional qualification of contractors and owner-builders, s. 6
Towns where at least 5 businesses whose licence includes subcategory 16 are based (the figure is how many).
A summary of public data and the law, not legal advice.