The story started with a family (maybe French) living in a remote island (?) They were discussing the new X-bomb experiment planned by one of the global powers.
On the day of the experiment, they felt something wrong and heard from the radio that an bomber was effected by the experiment and dropped an X-bomb on the North Pole.
Hours later, the tide came and never stop rising. They decided to get on the family yacht. Sea level kept rising and they had to abandon their house. When they sailed out to sea, the radio was silent.
After drifting/sailing for sometime, they finally found an island and landed. The island was apparently a previous peak of a mountain. They then settled down and started to raise crops, making soaps, ..., etc.
That's all the details I can remember now.