。
She has the ability to speak and write French.
Literal
She [topic-は] French [object-を] speaking and writing-ing-doing ability [subject-が] there-is.
This sentence packs two grammatical patterns: ~たり~たりする for non-exhaustive lists of actions ('do things like X and Y'), and the relative-clause-modifying-能力 structure where the entire 話したり書いたりする clause attributively modifies 能力 ('ability'). 能力がある ('to have ability') uses が because 能力 is the subject of existence. So literally: 'as for her, the ability to do things like speaking and writing French exists.'