“Justification de domicile” means proof of address in French. If you need a fast-track, just ask a local friend staying in France who already pays electricity (EDF) to include your name in their utility contract. They could easily do it online. It’s a simple process. You suggest him to log online to his account and add you on the contract and then print the ‘attestation de contract’ it will take about 15 days but if the same person calls directly it can be available for print and updated the same day. Then with this document that has your name on it, you could present it as proof of residence.
Gabriel offers extended assistance and advice to foreign entrepreneurs who are trying to settle down in Paris. Contact him at his website.