Just a minor quibble - it's not the 'red passport' that is important - it's the proof of valid rabies and/or other vacs, duly stamped by the vet, contained within the pet passport that is important.
The question will be whether you have time to get your doglet naturalized as a Swiss (canine) citizen before your trip to France. Here are the rules for bringing a pet into France from an EU state, or for travel within the EU member states (Switzerland included):
http://ec.europa.eu/food/animal/live...m_intra_en.htm
(Even if you have the little red pet passport, you may need to bring along your SA docs as well, as those would have your most recent rabies vac. info.)
If your doglet is still a South African citizen (i.e., you haven't had time to get the pet passport), then essentially it's the same process as bringing your dog into Switzerland. The regs are here:
http://ec.europa.eu/food/animal/live...m_third_en.htm
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Be aware that France has enacted BSL, breeds in category 2 face restrictions, breeds in category 1 may not be imported.
http://agriculture.gouv.fr/animaux-dangereux
http://agriculture.gouv.fr/IMG/pdf/0..._dangereux.pdf
(I have no idea how this is enforced on the ground, though...)
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That said, I have generally encountered pretty lax - or no - controls crossing the border. Nonetheless, I always have my dogs passports at the ready, all vacs up to date and conditions met. Just in case. I would advise anyone crossing the border with pets to make sure all docs are in order, all requirements met.
Hope your doglet has a safe journey, and may you all enjoy your Swiss adventure!