According to Wiki France has played 21 nations - Australia, Canada, England, Fiji, Georgia, Great Britain, Ireland, Italy, Jamaica, Lebanon, Morocco, New Zealand, Papua New Guinea, Russia, Samoa, Scotland, Serbia, South Africa, Tonga, USA and Wales. They have also played teams like the British Empire XIII and Other Nationalities.
This is compared to Australia - 14, England - 15, Great Britain - 6, NZ - 12, PNG - 13, Russia - 17, USA - 18, Ireland - 19 (played Cook Islands, Malta, Moldova, Spain which France have not), Italy - 20 (including Czech Republic, Germany, Greece, Ukraine) and Lebanon - 21 (including Canada, Japan, Niue)
For national opponents France and Lebanon look to have the most. For overall opponents England would go close since they've played several teams like NZ Maori, Cumbria, CAS, Exiles etc.