I wondered why "salire" meaning to go out sounded vaguely right to me, and it eventually came to me: "sally", as in "Sally forth!" and "sally port" (regarding which last, Wikipedia relates "sally" in the military context to "sortie" in the same context, which makes for a nice etymological dovetailing).

Not that that'll help keep track of the sense, since both sally and sortie have fairly narrow uses in English. But a sally port is a particular type of exit, (though its characteristics probably hinge more on its use as an entrance).