Well I am in dilemma. I am not French citizen and have to catch a flight tomorrow at 13:25 France time. I intend to reach there by 12.
What is the best way to reach Paris Orly airport from Rue Mirabeau?
Best as in "simplest, most convenient": call a taxi. It'll take anywhere between 20 and 50 minutes depending on traffic, and will cost you 39 to 42 euros (35 euros flat fee Paris Right Bank to Orly + 4 or 7 euros booking fee). Alternatively, Uber, LeCab, Chauffeur Privé, etc. (prices vary). Taxis have the advantage of being able to use bus lanes, but that should make little difference on this specific route.
A few public transport options: