With no internet there's no mail, no whatsapp, no Visa/Mastecard and also no Bitcoin.
But you were expecting this answer.

But the internet is a complicated bunch of interconnected networks. Falling the whole internet is highly unlikely, and for those affected by the failure, bad luck.
It's already rather difficult/unlikely to have a failure for more than a street or a town and in the future it will become even more unlikely.
Also big companies do use the services of multiple internet providers, if one fails the backup is used in seconds.

All in all, there's maybe a chance that your wallet will be not useful for a while, but for the whole Bitcoin to fall due to whole internet going down, no, the chance is slim.
Maybe solar explosions can do that, but then Bitcoin will be the least of our concern.