"The sitting woman is thinking" - wouldn't it be a more natural order?
In this case 앉은 is correct.
앉는 여자 a woman who starts sitting.
앉은 여자 a woman who is aleady sitting.
앉은 is better to say instead of 앉는.
From what I understand, 앉는 is correct as it's not referring to the verb 'to sit' with the topic marker, it's referring to 'sit' as a noun and using 는 to show it in the present tense. 앉은 would refer to past tense.
앉는 is not a noun but the present determiner form of the verb 앉다. It acts effectively as a noun-modifying adverb in English.
The act of taking a seat is 착석.
앉아 있는 여자가 생각하고 있어요.