I have found what I believe to be 3" galvanized pipe running through the middle of my backyard, which used to be an old alley way that was closed approximately 50 years or so ago. Anyone have any ideas what it could have been for and how best to cut it out? This pipe is in my way of putting in a French drain.

Sawsall (reciprocating saw) and 9" metal cutting blade.

Don't know about your location but in PA, you are required to notify a central utility phone number (called One Call here) before any excavation takes place. And that includes excavation on privately owned property. All possible utility owners are notified (by the administrators of the system) and are required to respond within a specified time to determine if their records and/or investigation on site indicate that they have any facilities within the planned area of excavation. The property owner or applicable excavator has some protection once proper notification is made and clearance to excavate is given through the system. This having been an alley would increase the possibility of some facility having been placed there. It may be abandoned (unused) or maybe not. Was an easement maintained when the alley was closed?
And how does it interfere with a proposed french drain?

If the alley was a utility easement at one time that pipe could have been a city water main. As Harold suggested, use a Sawzall (reciprocating saw) or a cutting torch to cut the pipe, good luck, Tom

Most municipalities have laws that say you must notify your local authorities before you dig, or destroy lines you find under your property, so I advise doing so to err on the side of safety and law and find out what this pipe is/was for and is a dead pipe before you cut it out.