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She talked her husband into spending their vacation in France.
Literal
She [topic-は] holiday [object-を] France [in-で] spend [so-as-to-ように] husband [object-を] persuaded.
The pattern '[clause]ように + verb of telling/asking' is how Japanese reports requests, instructions, or persuasions indirectly. Most learners first meet it as ~ように言う ('tell someone to'), but the same frame works with 頼む ('ask'), 伝える ('convey'), and here 説得する ('persuade'). The reported content (休日をフランスで過ごす, 'spend the vacation in France') sits inside the ように clause; the verb of communication is what acts on someone else. The husband, marked with を, is the target of the persuasion.