[sc_rufctr]

If you want to keep your car completely original it's not a bad idea. The thing is getting the carpet off without wrecking it.
The glue is not particularly strong but the carpet and glue are old so go slow and use a heat gun with caution to soften the worst parts.

Ok... So it's out now. Now you have to clean up the old glue from the car and carpet. Then clean and reinstall. It's certainly doable but patience is your best friend.
3M sell some good glues for this job. Not sure which one but their web site would be a good place to start.

Incidentally a friend did the same thing with his headliner. I helped him.
It took ages to remove and clean but the end result was very good. It looks like it was never touched and factory fresh.