Velib' of course !
Your chance there is a "velib' station" just beside the apartment.
No excuse, then ;-)
Honestly, it worth the try. It is easy (not the first time... sorry), quick and not expensive (if you respect few rules of course).
Wait for a sunny sunday and jump on a velib'. Trust us you will discover Paris again.
My advice, save this 2 address in your browser's favorite, you will no more loose your time to find a bike.
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But.... please read the rules before starting or your bike will finish like that...