Very interesting thought. I believe that chains would initially split, effectively being forks of each other. However, the consensus algorithm of Bitcoin dictates that the chain with the most work is the valid one, meaning that in the event of a "reconnection", one of the chains would be abandoned (and everyone would agree which one to keep, namely the one with the most work).

In the case of a total disconnect between countries, there is no other way than splitting the network. If partial connectivity exists (using satellites for example), transactions could still be broadcasted from one country to another. However, the same coins could be double-spent in your own isolated network as well... until a reorg happens upon reconnect.