。
She has a feeling she wants to get married.
Literal
She [topic-は] want-to-marry feeling is-doing.
Two layers of hedging stack here. ~たい is the standard 'want to' suffix, but here it's nested inside ~気がしている ('has the feeling that...') for a softer, less assertive flavor — not 'she wants to marry' but 'something in her is starting to feel that way.' The continuous form 気がしている (vs. plain 気がする) frames it as a slowly forming state. The whole construction sidesteps the limitation that Japanese normally only directly asserts the speaker's own feelings — 気がしている lets the narrator describe a third-party's mood as visible signs without claiming to read her mind.