Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Fix Tension
TENSIONTAG_FIXParameter: Mode
TENSIONTAG_MODEParameter: Clamped
TENSIONTAG_CLAMPEDParameter: Amount
TENSIONTAG_AMOUNTParameter: Fold Map
TENSIONTAG_FOLDParameter: Make Map
TENSIONTAG_MAKEFOLDParameter: Stretch Map
TENSIONTAG_STRETCHParameter: Make Map
TENSIONTAG_MAKESTRETCHParameter: Selection Tag
TENSIONTAG_SELECTION