There are two types of specially marked K4P TC (or at least there have been in the past – I haven’t done most of the Pesach shopping yet). One is the regular plastic jar with a Gefen sticker (Volover Rav’s hechsher) as an extra seal over the container (the kind zdad would have a fit about).
The other is the old fashioned glass jar with Rav Charlop’s hechsher. It’s manufactured somewhere in the Americas.
The regular TC is on approved lists as well, even without special Passover certification.
Decaf always needs special Passover certification.
I don’t know if French Roast is included in the approval; from the way the list is worded, it seems not (but I wouldn’t be surprised if it was).