There are not all that many integral pitch tents because they are more difficult to design and some, in particular Americans, like the idea of having just a bug net up (inner mesh tent) for views and that cowboy like experience.
Tarptent and Hilleberg are two of the brands that do integral pitch.
Freestanding.
The GR20 is indeed a rocky area (not that I have been there but do know what it looks like) but as much as having a freestanding tent lets you move it around once set up, you still need to anchor it down so in the end you have to peg it down if you don't want to see it flying away.
Many will use stones over the pegs given that stones are everywhere there.
Given that you have been looking at two person tents for the extra space , a lighter (about 1400g all up) but still large enough shelter could be the Tarptent Scarp 1 (I am part of Tarptent...)
That is an integral pitch shelter, two doors and symmetrical so that you could pitch it right against rocks or close to another tent on one side and get out of the other and still have the choice inside of where to have head and feet. (some tents force you to sleep one direction)
The tent needs a minimum of 4 pegs, works best with 8 but only 4 need to be in a particular spot.
Easy to pile rocks on top of those 4 corner points and or use an extension to wrap the cord around larger rocks.
Can take two mats , so more than large enough for one. (a 6'4" person will fit in on top of a large thick mat ...)
This is a photo of one I was seam sealing in my bedroom :

should illustrate the point about rocks instead of or on top of pegs (note : best to carry some small Chux for that so that you don't damage the cordage when smooth rocks are not about. Chux are very good for drying things, like a wet tent and I use a Super Chux as a towel)