I think the file is normally called sessionstore.js (although it only contains valid JSON).
If there is data you may want from the file, you should make a copy of the file to preserve it before restarting Firefox. (I'll assume you've called the copy sessionstore.bk.json).
Accessing the data from the terminal.
Note: This section focuses on Unix-like OSes (Linux, Mac, BSD). If you're on Windows, you can either use a Unix style terminal (eg. Git Bash, MSys, etc) or adapt the instructions to a Microsoft terminal. (For all I know, they might even work as is in Powershell; I'm not familar with it.)
You can pretty print the file to make it readable, and search and copy data using either your terminal pager or a tool such as a text editor. A couple of good command line tools:
Python's json module comes with the command line json.tool. For instance, on a Unix shell, the following command will save the file nicely formatted:
cat sessionstore.bk.json | python -m json.tool > sessionstore.pretty.json
or the following command will let you read it in the terminal pager:
cat sessionstore.bk.json | python -m json.tool | less
Node.js's underscore-cli command line tool. If you install NPM, you can then install underscore-cli with the command
npm install -g underscore-cli
Then you can pretty print in colour to the terminal pager with the command:
cat sessionstore.bk.json | underscore print --outfmt pretty | less
Accessing the data with Python.
If you have a basic familiarity with Python, you can import the data into Python as a dict and access it using the standard methods. For example:
import json
f = open("sessionstore.bk.json")
data=json.load(f)
# print a list of top-level JSON entries
for key in data:
print key
Most other languages should have similar libraries available for importing JSON data.
Accessing the data with a dedicated JSON viewer.
You could also use a JSON viewer application. A couple of possibilities: