These are known as Transporter Bridges and there are still a few in service.

http://en.wikipedia.org/wiki/Transporter_bridge

I later started wondering how nasty it had to be, during strong winds, to travel with the AERIAL FERRY which consisted of a platform hanging from the bridge on its long-long wire ropes.
The sways must have been significant!!

The bridge was called "TRANSBORDEUR".
The bridge had an AERIAL FERRY hanging from the bridge and traveling , slightly above waterline, over the bridge full span.
(source: Google: Wikipedia)
I now fully believe, that the AERIAL FERRY (for use by pedestrians & vehicles) is the right answer to the query of how the bridge functioned.

Any idea how that bridge functioned?