Need to reseal exterior french doors!

[kunstler.bill]

Hi! We've had some leaking under the frame of our exterior french doors in our bedroom. It leaked under the carpet onto the subfloor and caused some mold. We're having it cleaned, but I obviously need to reseal the outside area under the door sill, ie between the sill and the stucco of the house. It looks like there is some kind of caulk or seal there, not sure exactly what kind. My question is what is the best method to remove the old sealant between the sill and the stucco and put in some new sealant and what should that sealant be? Also, at least on one side of the interior area where the subfloor meets the door frame, there is some old cracking interior seal as well, but I have no idea what kind of product it is. I'd love to seal it from both sides, what is the best kind of interior product to use where the wooden subfloor under the carpet meets the door frame? I'm including one pic of the interior old sealant, and another of a different exterior door of my house -- the leaking one is covered with a tarp so I can't get a picture. But the picture of the area between the sill and stucco is very similar except it's higher up and doesn't have any caulking. The leaking one in question is lower and does have caulking, albeit old and cracking. Appreciate all and any help, thanks!