Hi, Patrice! Your soil looks like it has lots of clay (anybody else think so, or is it just me?) The nice thing about sheet mulching is that you can add all kinds of things ... a layer of sand, a layer of compost (these two are especially important if you do have heavy clay soil), bone meal, leaves, thick overlapped newspaper or cardboard to act as a weed barrier ... All of these things break down together, worms and other soil critters move in and stir it up.
You can plant right into the layers, water the seedlings well, and bring the cardboard/newspaper right up close to the plant to keep out weeds. By next year your soil will be much improved and you won't have dug up a singe spadeful of dirt.
Building a raised bed and filling it with compost and soil is another great way to counteract your clay.
Depending on what you are intending to plant and how thick your sheet mulch is going to be, you can either:
dig holes beforehand and mark them, so you can put in things like trees and larger shrubs; OR
simply push aside the sheet mulch where you intend to plant and cut through the cardboard (if you used it to block weeds) with a utility knife, so you can put in seedlings and small shrubs; OR
plant directly into the top layers of the sheet mulch, for all herbaceous plants and seeds.
The cardboard is optional, depending on how deep the other layers of sheet mulch are. The point is to block all possibility of the grasses and other undesirable plants underneath growing up through the mulch.
I was able to get a lot of free mulching materials from neighbours, including four giant square bales of spoiled hay, lots of leaves from last fall, and mixed manure and bedding from horses, goats and chickens. We also paid for a few loads of chipped wood (perfect for the final layer to block out new undesirable seeds). I would guess that you could easily do the same in your area. A trailer is a good investment if you don't already have some means of hauling materials.
Bonne chance avec tous vos projets! J'ai hâte de voir le progrès!
If you have plenty of cardboard and other organic matter then sheet mulching is the way to go. I garden on heavy clay and that's the way most of my beds were created. If your back is up to it, forking it open beforehand will help. I'm not sure about adding sand. I've heard of people adding sand and having their clay soils turn to something like concrete. It has to do with the composition of the clay. Perhaps try some sand in one area and see how it goes.
As suggested below because you have quiet a bit of clay I would just throw as much of mulch material you can get your hands on. Plan nitrogen fixing and high bio-mass plants. Come the fall you could always do a run around the neighborhood for any garden bags you see.