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This serves as a link between French clientele and the foreign company, giving you the chance to study the French market and promote the company's products. Employees cannot legally act on behalf of the company.
This legally forms part of the foreign company and can operate by itself and issue invoices directly. In the case of a permanent set-up, it must establish its own accounts.
This is a company with a separate identity, legally independent and fully subject to French law (both general and tax).