Daylight Savings Time (heure d'été, sommerzeit) was widely used in WWII (even by the US, where it was called War Time). Britain set up (1940) GMT + 1 all year round, then (from 1941 to 1945) added an extra hour in summer, so GMT + 2. (In other words, the UK was on CET, CEST). See this page in French for a full table of annual UK changes. (UTC = GMT).

The same link gives a table for France. For the WWII years, Vichy zone times are given. They were the same as the UK and Germany, ie GMT + 1, GMT + 2. (= CET, CEST).

However, in all German-occupied territories from 1940 to 1942, GMT + 2 was applied all year round. So inhabitants of the French occupied zone (and no doubt Belgian and Dutch too?) jumped from their normal winter time (GMT) to GMT + 2. Paris à l'heure allemande wasn't metaphorical in the first instance.

There was some confusion after the war. Wikipedia says this:

In 1945, Berlin and the Soviet Occupation Zone even observed Central European Midsummer Time (Mitteleuropäische Hochsommerzeit, MEHSZ; UTC+3); in 1947, whole Germany switched to midsummer time from 11 May to 29 June.

Hochsommerzeit = the high summer time mentioned by DoDo above. The point for the French decision was that Berlin time in 1945 was going even further away from GMT. France at that point was still fighting for its independent existence and was extremely prickly about administrative symbols. So the choice was made (just when the UK was moving back towards GMT) to take a middle path, ie GMT + 1 (= CET) all year round. Neither London nor Berlin...

1945
    Abandon de l'heure d'été pour rompre avec "l'heure de Berlin" imposée pendant l'Occupation. Le décret du 14 août 1945 fixe l'heure légale à GMT + 1 heure, solution de compromis entre l'heure allemande (GMT + 2 heures) et l'heure de Greenwich.