Without internet we can go back to the bronze age quite fast.
Realistically however, attacking some undersea cables isn't a threat to the existence of the internet anyway. Even if you could split THE internet into many national/regional networks, that would still be sufficient for most industrial and economic needs. More expensive and robust links could connect these regional networks where truly needed.
This is not the specific case, but I think that if Europe lost access to US internet services its economy would collapse.
Not saying that the loss worldwide free communication wouldn't be painful, but I think it would be as painful for both the providers and the consumers of services.