According to this (somewhat dubious looking article):
Since it is so light, the FlyNano falls under the weight of what is considered to be a plane, so in most countries you won't need a flying license to take this baby to the skies.
The aircraft weight needs to be 70 kg or less. FlyNano mentioned this on their FAQs page (my paraphrasing):
Do I need a pilot's license to operate FlyNano?
According to the European Aviation Safety Association regulation ... FlyNano is below the necessary weight of 70kg ... In Finland for example no classification, no aviation license or medical certification are needed. But skill is needed. Nevertheless a good understanding of water plane operation, rules and aviation safety is requested. ...
I found that any aircraft less than 70kg is not affected by EASA regulations. But regardless, and emphasized by FlyNano also, pilot skills are required.