Prof
the Wiki link I gave above gives details across a range of engines arising from the Ford PSA joint venture. As regards the car under discussion the C5 both Mondeo (world car) and C5 2.0 litre diesel used Aisin 6 speed auto. It makes good sense if you are using the same engines to match them to the same gearboxes. Albeit control characteristics may vary. There’s lots on Wikepdia if you search Citroen C5, Ford Auto transmissions, Aisin automatic transmission and PSA auto.. The Aisin is a well regarded unit used in Mondeo, FL2 and a wider range of cars. The strange thing that I found was that using the same 2.0 diesel the auto Mondeo had a far better towing capacity than the C5 with ostensibly the same gearbox. This was in 2010. This gave rise to quite a discussion in another forum where a Citroen owner detailed the marques quirky approach to towing specification.
Other than the joint engine venture and the sharing of the Aisin gearbox I was never aware of sharing of body parts etc. But such is the commonality these days it’s quite likely that there could have been common parts from other suppliers but not as a formal arrangement between Fore and PSA.
PS Edit. The Aisin gearbox in the C5 is likely the TF 80 450nm. Same as Mondeo 2.0 litre tdci, and the XC70 2.4 5 cylinder AWD. A well regarded gearbox. Shortly after Ford moved towards Powershift a dual synchro clutch type.