How can I access the folders where Firefox mobile stores its application data
Apps on Android store their data in /data/data/[package_name],
so Firefox should be keeping its data in /data/data/org.mozilla.firefox.

NOTE: To access this directory you need root access. 

Use file:///data/data/org.mozilla.firefox/ from inside Firefox to access the folder (without root). This work because Firefox owns the folder (see the comments)