The main character in the movie has started to fall for the heroine.
The lead actor in the movie has really started to like the main actress.
この場合、次のような言い方ができますよ。
ーThe main character in the movie has started to fall for the heroine.
「映画の主人公はヒロインを好きになりつつある」
to start to fall で「（恋に）落ちはじめる」
ーThe lead actor in the movie has really started to like the main actress.
「映画の主演俳優は主演女優をとても好きになりつつある」
to start to like で「好きになりはじめる」
ご参考まで！
カナダ 
