The Nazis had a pretty far-reaching "Germanization" program for people they considered ethnically acceptable, like Poles of partial-German descent. They were sent to Germany to learn the language. Other Poles were considered untermensch and fit only to be slaves or exterminated.

How this policy would have applied to people like the French I don't know, but the Nazis seemed to have been pretty keen on spreading their language and culture to conquered areas.

I'm fairly sure that the plans for Europe after the war was for a new German superpower, who's borders would stretch from the Germanic lowlands in the Netherlands to the Ural mountains in Russia. Those of Germanic descent (Danes, Swedes, the Flemish, some northern Italians, etc.) would have been encouraged to breed with "full blood" Germans, as they would all be under the "Aryan Race". All those in the "Gross Deutsche Reich" (Greater Germanic Reich) who were not of Aryan descent would be deported or killed, part of the Final Solution. The only Germanic peoples who would not become part of the Gross Deutsche Reich would those of the British Isles, who would instead become great allies, who would eventually defeat the United States (This was one of the major goals of the invasion of the Soviets, to force the British to surrender, besides Lebensraum and destroying Communism). This English ally would be much like the Prussian ideas for Austria, with constant war over German hegemony before they were allies in the First World War.

The land stretching from the pre war borders of Germany to the Urals would be used as "Lebensraum", or Living Space. This would be were the Aryan peoples would settle as colonials and eventually the Aryan race would propagate into huge numbers, perhaps billions, much like the Indian or Chinese race. However, during the war, Hitler had a lot of trouble convincing people from the Netherlands, Denmark, Norway, Sweden and Austria to join his selected Germans in Poland during the war as colonists, so the plan never propagated well and then the war was finished quickly after that.

In terms of a European Hegemony, Hitler envisioned a future where Europe was led by the German peoples and others were encouraged to "live like the Germans". France would have been a shell of it's former self, completely under German military control, whilst Italy would be a firm ally who had control of the Balkans. Japan would have been the only ally for Germany which was outside of Europe, who would keep the power of America and the Pacific in check, while the U.K would control Africa and India.

In all, Hitler had very few plans for Germany outside of Europe beyond an alliance with Japan and America eventually become either a subservient nation, or being punished into oblivion.

This would depend on the country, it wasn't uncommon in this period of history for an occupier to enforce it's culture and language upon an occupied people. The USSR did it in various places trough education, this would be called Russification. The Third Reich had a comparable policy in occupied Luxembourg a good example being that roads would be renamed from French to German. However, for as far as I know they didn't try to do the same thing in The Netherlands or France.

In conclusion: Depending on where you lived you indeed could have been speaking German if it wasn't for '''them''.