Just spent 2 days developing a regular HTML, CSS yadada website for a client, and now she's telling me in needs to be on WordPress. Does anybody know a free way to add WordPress Content Management? (she won't pay)

It's shame you didn't get 50% up front and a contract. And proper written estimate and project spec. All these things are protection for you and avoid shit like this happening. If you have no paperwork you're fucked. Tell her you can redo it in Wordpress but it will cost xxx. If she doesn't want to pay, simply tell her to fuck off.

Couch cms might be an option. Just add tags to static site and it all becomes editable.
Or just send quote for how much to convert to wp

I agree with helloworld. Always make sure you get 50% up front. Make a document and describe the scobe of the project. If something falls outside of the scobe it easy to tell the client and to understand for the client.

There is not really a way to convert the site to Wordpress for free. So if she does not want to pay, don't do it.

@helloworld it's my first freelance job, live and learn I guess! But thanks for the advice I'll be sure to do that next time

Yes, in the future get signed off requirements document, contract... She should have indicated Wordpress. I bill at 1/3 project points.
There are CMS plugins.

Would downloading a free theme, deleting all data and uploading my data work?

@magis A great place for digital contracts which are pretty cool, something I use all the time now.
https://www.hellobonsai.com/
For invoicing I use https://invoicely.com/