The official language of the Russian aristocracy and the court was French so it makes sense that they wrote in French....
I know they knew French, but Felix had mentioned before in his books that he disliked the practice of Russians speaking to each other in foreign languages instead of Russian and that he and his brother annoyed 'old ladies' by answering them in Russian when asked a question in French. Because of that it makes me wonder why he'd write to his own mother in a language other than Russian, unless it was to sneak things by the censors (which they had mentioned in some of the letters)
Also, on the subject of 'no specific names' being mentioned, there is a reason for that too. Zenaida wrote to Felix and Anna Rodzianko in a 'code' where terms or silly nicknames were used to describe a person they didn't want anyone to know who they were talking about. Rasputin was 'the book', N and A were 'aunt and uncle', Nikolasha was 'Luck', and more. But in other letters Ella was referred to as 'aunt's sister' so again she may not have been the person mentioned. Whomever it was, they must have felt there was reason to avoid putting her name, and probably assumed the other would know who they were talking about anyway.