"Your site font” isn’t working on my website.

In order to have the “Your site font” working on your website, the font family and tags have to be defined on the website’s theme. This means you’ll need to make sure h1 has a font family and style assigned, the same goes for h2, h3, p, etc. 

If you see the fallback Times New Roman font where you expected to see your site font, it means your font family and tags haven't been defined on your site's theme.