Be sure to remove the drive side crank arm first.
the bright lock ring will remove anti clockwise. Almost always holding the adjustable cup is not needed for removal but will be for installation.

the fixed cup ... it is a later bike it appears could be Regular or LH thread. Old French was regular RH threading 35x1, later... Swiss LH 35x1 or English 1.370 x 24 LH.
the fixed cup may be best a bike shop task if you do not have the tools.

j