The World at War, the battle of France was now over

The World at War, Episode 03. France Falls (June 1940)

Narrator:  In the words of Winston Churchill the battle of France was now over, the battle of Britain was about to begin. 

Patxi: (...) but I am wondering if reported speech rules are not applied. (...) I mean the use of now with a past tense instead of using other time adverb like then for example.

The rules of reported speech are followed in the verb. He said "The battle of France is now over." The quote changes the verb to 'was' and that's fine. You're confused because you're thinking the time expression should also change, perhaps to 'then' but in this context that would be strange.
Neil. Learning English, British Council.

Thank you very much, Neil, for your help.