Sheila Wilson wrote:
You DO have to declare the income to the French authorities in the normal way, even if the money isn't paid into a French bank account. If it's in dollars you'll need to use the correct tables to convert it to euros (probably the Banque de France but I don't remember the applicable date - invoice, receipt, month end, quarter end...).
And state your invoice in both currencies. => easy for the client and for your own accountancy.