American/French couple moving to Malta?

Hi,

My fiance and I are considering where to live in the EU after our marriage. For various reasons, Gozo seems like one attractive possibility. We have savings and I have some self-employment as a teacher/editor. However, we would ideally like to work there or start a business.

My question is about my legal right to stay there. We plan to go to France and get married, which might take up to 2 months to sort out. At that point, I know that if I wanted to live in France I'd have to go back to the US to get a long-stay visa. However, my understanding is that with EU laws, the wife of an EU national can move freely with him. So, I'm confused about whether my husband and I can just come to Malta with the marriage license. I wouldn't want to overstay my "3 months in Schengen out of any 6 month period." But maybe with the marriage, this rule immediately disappears and I can stay with him in the EU without a visa (but ironically not in France without a long-stay visa)?

Once in Malta, I understand we'd have to get some kind of work permit and/or temporary residence permit. But I'm confused about exactly how to get it and what documents or financial support would be necessary. As I said, we are not destitute and do have some self-employment options, but at the same time, we're not retired and definitely would like the right to work in Malta as well. As the wife of a French man, would I automatically have the right to stay there as long as it takes to figure it out? If there are important time limitations I need to be aware of, I better plan accordingly.

Thanks!