This answer is a bit vague... but will help you to do further research. When the Nazis invaded France, they occupied the south, and the north - which was called vichy France, was supposedly 'free France' (but was still very nazi). marcheal petain was the leader of vichy France, he was called a collaborator for this as he complied with all nazi ideology. If you research Petain, and collaborators you will get more info... this is just what i can remember from my research. You will also, when reseraching vichy France, find a map which will show the occupied and vichy France divide.
In the UK, Neville Chamberlain
John Curtin - to participate in the defence of Autralia after the Japanese entered the war in 1941, rather than leaving them fighting in a European war.
Robert Banks Jenkinson, 2nd Earl of Liverpool, was the PM during the War of 1812.
20th January 1943 at 12:30 pm
Winston Churchill succeeded Neville Chemberlain in May 1940
Peter Fraser .
In Great Britain, it was David Lloyd-George.
Winston Churchill was PM during WW2 : 1940 through 1945.
From 1911-1920 the Prime Minister of Canada was Sir Robert Borden.
Peter Fraser was the pm of New Zealand during WW2 however, New Zealand did not take part in the war.
In the UK, Neville Chamberlain
H.H. Asquith
John Curtin - to participate in the defence of Autralia after the Japanese entered the war in 1941, rather than leaving them fighting in a European war.
Clement Attlee
King George VI was king throughout World War II.
Your question needs to be more specific. More than one country was governed by a PM in WW2. Great Britain had three (Chamberlain, Churchill, Attlee) during the war.
Robert Banks Jenkinson, 2nd Earl of Liverpool, was the PM during the War of 1812.