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She didn't marry him of her own free will.
Literal
She [topic-は] her own will [by-で] him [with-と] married [it is not-のではない].
~のではない ('it is not the case that X / not by X') is the negative of the explanatory ~のだ. Combined with the framing 自分の意志で ('of one's own will'), the sentence denies the means of the marriage — she got married, but not freely. 意志 ('will, volition, determination') vs 意思 ('intention, opinion'): both readings いし; 意志 leans toward strong will and resolve, 意思 toward a more neutral 'intent.' Here 意志 carries the stronger weight of personal agency.