Can my online form be "based" in Europe? Do you have European sites?

Yes, you can. Just simply access My Account - Settings page and check "Europe Datacenter"

https://www.jotform.com/myaccount/settings

After checking the option, your forms and data will be moved to our Europe Servers. 

You can read more about this feature in the following links:

https://www.jotform.com/eu-safe-forms/

https://www.jotform.com/blog/178-EU-Safe-Forms-Our-Solution-to-the-EU-Safe-Harbor-Invalidation

Should you need any further information, please do not hesitate to contact us again.