DVDxDV and Streamclip can both "rip" your old burns back to something Final Cut will recognize.
DVDxDV is much easier to use, but it cost money.
You also need to know that compressing video for a DVD is a destructive process. DVDs never look quite as good as the original show export, and ripping the DVD sends you through that process twice.
DVDs are not good for archival storage. You may find that you can put a new fresh graphic into the show and it won't match the graphics that were already there.
Koz