It makes sense to me that there are rules around admitting cars to the road. In the case of California I find these rules are extremely easy. For example, my '72 Fulvia was approved last week without any safety or technical inspection. It does not even have any seat belts, despite those having been present originally. In France my Pagoda must pass a strict safety and technical inspection every 2 years. In California, only emissions are tested for 1976 and later cars.
Any way, the DMV and CHP ruled last week that the Fulvia does not need a Federal emissions label and is also otherwise A-ok. I received a CA registration and plates. Hope your trip to your DMV will be equally successful.