If you're a founder of a startup working full-time and unable to pay yourself a salary yet, can you receive unemployment? (Maybe you would count this as "underemployment"?) What if you left your previous job voluntarily?
No but there are grants you can receive for starting companies that lets you pay yourself a low-ish salary for 6 months when starting up. This was extended to 12 months during COVID I believe, unsure what it is now.
In France, yes. You can apply to get the money you would receive in unemployment benefits as an initial capital in your startup (for paying yourself or for other expenses).