SOLVED. YA Sci-Fi or Adventure: Global catastrophe of ocean rising due to super bomb testing. The world turned into a huge ocean. Family takes on a sailing boat to find a new place to live. They finally found an island that had been a high mountain top.

[Jack]

The family might be a French family. They got on the family owned sailing boat in time to escape the flood. There was also an aged uncle with the family. The uncle was a scientist and taught the children how to make soaps.

The catastrophe was caused due to a chain of disasters. A test of a new secret super bomb exceeded the expectation. An airplane carrying the 2nd super bomb happened to be on the North Pole and its bomb was also detonated by the side effect of the 1st bomb. The whole North Pole melted and the ocean level rose quickly. The family escaped by taking on the sailing boat right next to the house. The world soon sunk under the water.

(Not so sure) the family met some local residents eventually but couldn't understand each other until they found a dictionary someday.

This was translated and shortened in Japanese around 60s~70s. The original novel might be published between 1930s~1970s. It might be a French novel.

The last name of the author might be: Duhamel.

[Jack]

Found it.

Les voyageurs de l'espérance - récit de l'âge atomique