I would recommend doing as much research as you can - our page on Moving to Valencia is a good place to start as a general overview. This list of Pros and Cons of Moving to Valencia may also be useful.
You could try Googling for blogs of expats in Valencia to get a real idea of what it's like to live there. Also, if you have a look at our Expat Experiences in Spain page, you'll see there are a handful of expats living in Valencia that we've interviewed, so those are worth a read.
As an EU national it should be relatively easy to move to Spain - you should only need your Irish passport. However, I would recommend double checking any documentation requirements with a local Spanish embassy or consulate before leaving.
As for health insurance, I would recommend contacting some international health insurance companies directly for a quote.
Best of luck with the move!
I've searched online and can't seem to find a definitive answer to your question - I think it would be best if you can contact your local Spanish embassy, or a French immigration authority, for clarity on this.
Best of luck.
I don't live there myself so unfortunately I'm not able to answer some of your questions. We have a page on Accommodation in Spain, though, which is focused on finding a place to rent and has some good tips. I also found an article by an estate agency about the process of renting and what documents are required - you can click here to see that article.
Hope this helps. Best of luck!