The battery died recently on the key FOB for my 2007 Grand Marquis.  I replaced the battery and it still didn't work.  I messed around with it, searched for new ones, and finally came across this website that will tell you how to reset almost every key FOB imaginable.  I'm thinking that the info may be in the User Manual for the car but I didn't think to look.  I didn't look because I largely didn't think out the fact that one would ever have to reset the FOB.  

Here is the website:

https://www.keyfobprogram.com/2007-mercury-grand-marquis-remote-programming/