You can fish all year but not all the fishes. In category 2 waters, predators fishing (with any type of
baits) is forbidden from end of january to generally first week-end of may. This concerns pikes and zanders mostly, but you can fish other fishes.
If you plan to fish the Seine, there aren't too many rules to know. Check the link Laurentdu76 gave you. If you need any other additional infos you can't find in english, send a private message. I'm not from that area, but I can help you understand the different french rules.
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