I seem to recall that the jack and handle were stored in the boot on an early 504 while on the later models they were stowed behind the driver side headlight. Is yours an early or late? What year?
Mine is a 1970 504 sedan. I believe it attaches in the engine bay, drivers side, Alpine seems right, there are some bits attached to the drivers side engine bay which I assume may enable the jack to be attached to it?
The "frame thing" in the earlier pic is the jack. The picture below is the jack on a late (1980 I think) 504. Note that the jack is secured via a clip attached to a spring. The earlier type of jack, as per the first pic, is secured via a screw on nut which is shaped like a washer with two lugs. In both cases, you will see the jack handle retained by a metal strap which is also retained by the same sort of flat washer type of nut.
It appears that jack storage may have varied over the years and also within the same year. I have looked at two late 504s from the same year and one has the jack stored in the engine bay as below, while the other has no sign of there ever being an attachment point for the spring and if memory serves correctly, the jack was stowed in the boot.
Yeah mine doesn’t have the frame but it has the spring as per arrow 2 And the jack itself looks similar to the one adjacent arrow 1. I dont have any pics atm moment but will get some next week.
Goodoh. So it appears that you have a later style jack. If your car is early, then it will most likely have a threaded stud as the top anchor point, on which the retaining "nut" is screwed on to. If so, then that earlier anchoring system is not compatible with your later style jack. If so, then that's probably why you can't work out how to hold the jack in place - the two methods are only suitable for one style of jack, not both.