We don't know much about Franziska's life before 1920, do we? She may have learned some English in Berlin before jumping to the Landwehr Canal, and even some French. I have met waiters who speak 3 or 4 languages and can't even write properly their own. As far as I know, she was from a region where she may have heard Russian often -so she could have been able to understand the language, but not to speak it.
About correcting mistakes.... mistakes by whom? A few former retainers, officers and so, who had lost their country or their families, who could have been terribly confused themselves and who weren't really close to the real Anastasia for a long time?
I have always wondered why in 42 years no one seemed to be interested in a meeting of the claimant with Anna Vyrubova, the only survivor who had really shared the family life intimately. I think she would have been exceptionally qualified to say "she is" or "she isn't", not certainly aunt Irene -the claimant first choice....
The fact that Mrs. Tchaikovsky-Anderson never said -not even once as far as I know-, "I want to see Anya", may mean something... If the claimant really "believed" she was Anastasia, that meeting would have been just a logical request. But she didn't asked for it.
Ms. Vyrubova didnt show either any special interest in the claimant -something quite peculiar for a person who was so close to the family.
Oh, I know Mrs Tchaikovsky wanted to meet the Dowager Empress... May be she or the people around thought Maria Fyodorovna, an aged women bearing such a tragedy, could become as confused the way GD Olga was at some point, not having seen her niece in so many years and after what could have been a terrible ordeal. But probably they felt -in the 1920's or in the 1950's- that a meeting with Anna Vyrubova would have been an absolute fiasco for the claimant.