My garage isn't finished; there's bare studs. I want to set up a french cleat system to store my tools. Can I do it directly against the studs? Or do I need to hang drywall or a sheet of plywood first?
I think this will work fine.
Make sure you use a spacer, of the same material as the cleats, on the bottom of any storage units so they sit flat on the wall (studs) so the bottom does not teeter in.
One issue is; For any storage unit that is narrower then the stud bays, the bottom of the unit will not have studs,"wall", to rest against. You will need to have a spacer on the unit wide enough to bridge the studs or add a furring strip in between the studs for a smaller bottom spacer to rest against.
There are many YouTube videos on French Cleat Tool Storage.
A french cleat relies on the cleat itself- placing a furring strip to further support is a belt and suspenders approach, at which point your cabinets could be screwed to those studs that are exposed and supported by the support strip. I prefer cleats as I tend to work by myself, and they make it easy to hang a cabinet solo. Your cleat will work fine on open stud framing.
A French cleat relies on two points of contact - the rail at the top and the cabinet's bottom resting on the wall (otherwise it would be prone to rocking in and out on the cleat). If the cabinet (or whatever you're planning on hanging) is wider than the stud spacing, it would be able to lean on the studs in the same way as it does on the wall.
I would suggest reinforcing the bottom of the cabinet in this case, to make sure that the bottom that spans the studs is rigid enough to support the weight (perhaps by adding a 1x4). This will also make it easy to use a non-flush French cleat which would simplify installation.