Primary corporate records rather than descriptions: share registers or certificates for both entities, the executed purchase agreement with its closing documents, director resolutions, and financial statements or contracts showing each company actively trading. A letter asserting that the companies are related is evidence of somebody's belief, not of ownership.
Ownership is proved in registers, activity is proved in invoices
Two separate propositions need documents. The first is the relationship: who owns what, in what proportions, on the filing date. That is answered by constitutional documents, the share register, the transfer instruments from the acquisition and the resolutions appointing officers, ideally accompanied by a chart that reconciles to those papers.
Where a parent sits above both companies, every layer needs the same treatment. The second proposition is that both entities are doing business, meaning the regular, systematic and continuous provision of goods or services, which is not established by a bank account, a mailing address or a website. Recent financial statements, signed service agreements, payroll summaries, occupancy records and supplier invoices carry that point.
Anything in French requires a complete certified translation. Assemble the two sets separately, because reviewers read them for different purposes and a bundle that mixes them tends to leave one proposition thinly supported.