A search for "brackets" would likely turn up more options than for "French cleats," a term I've never heard used. Brackets of the type shown in the PDF seem typical of many that might show up in a large hardware store. Alternatively, sources such as RackSolutions may have suitable parts. I, myself, would probably go to a sheet metal shop and have some made that were just the dimensions I needed, with holes punched where I wanted them, and made out of stainless steel so that they lasted as long as the house lasts.

kas

A french cleat is usually made of wood and used to hang cabinets.

Here is a link that might be useful: French cleat

Always good to learn something new.

In the first link, kitchensource.com shows a system that they call a French cleat that is significantly different in configuration than the Chad's Workshop second link shows. The first is potentially rigid; the second is not. I would think that a rigid system should be used for hanging a hood insert. And I would have called the first system 'angle brackets attached to a mounting plate.' The characteristic that seems to define a French cleat is the mating pair of 45-degree cuts that hold the hanging component in place.

kas

Ikea sells some "L" shaped stainless shelves that are hung on the wall with a metal french cleat system.

However, what the drawings show in the pdf for step 1 is screwing a big plywood 1/2 of a wood french cleat to the wall. They say that this mounting plate is included.

The insert is then screwed to the liner in step 2. In step 3, Brackets are screwed to the insert+liner.

Then, the insert + liner is attached to the cleat on the wall by screwing through the brackets in step 4. The brackets don't use the cleat at all.

Step 5 shows the other half of the french cleat mounted on the back of the decorative cover. It looks like they split the cleat into two sections with a gap in the middle. When they slide down again the wall, they are caught by the first cleat by the opposite angles.

I don't think they bought anything special. The metal of the liner is all you need to protect the wall.

Here is a link that might be useful: Ikeadom.

Okay, so I wonder if a person couldn't use some kind of L brackets, screw them to the wall framing and then mount the range hood to the underneath of said brackets? Maybe the whole mounting plate isn't necessary?

Many ways to satisfactorily achieve the goal. As for metal French cleats, here's one that Home Depot sells that's rated for 200 lbs.

Here is a link that might be useful: HD FC

What about just a Monarch Z Clip? They work very similar to a french cleat?

Here is a link that might be useful: french cleat

Sometimes, a pair of hangers have to be placed on the object to be hung such that they are not separated by the stud-to-stud distance in the wall (usually 16 inches in US housing, but often 24 inches is allowed with 6-inch studs. In such cases, installing suitable blocking in the wall before the wall is covered is desirable when the location of the object to be hung is known. Otherwise, a mounting plate or cleat can carry the load from the hanger locations to the studs.

kas