Many non phased array military radars do give height read out.
I wonder how they work? I know how it was done in the 1950s, with a "nodding head" radar, for the PAR approaches (or a similar mechanical implementation).
Perhaps you could ask your ATCO where this restriction is published. It doesn't appear to be in the slot coordination AIC, nor in a Supp.
I will ask.
essentially touch and go, then do an I from them?
If one could do a T&G that would be a brilliant solution to a lot of stuff, especially getting into the Schengen zone
Any French airport that offers that facility is going to get a lot of business