What is a french clete ?  I guess you could say it is a type of bracket that is super strong, and it's used for hanging extremely heavy things on the wall.  They have been used for hundreds of years, by ship builders and cabinet makers.   And... more than likely they were from France, but I've also heard that cutting something into small strips means "frenching" - like french fries.  Regardless of by whom or where they were invented, it's a super strong way to hang something really heavy on the wall without worrying about it falling.  So we use them to hang our Upholstered Headboards and Legless Tables on the wall.  Here's how to make one - 

Cut a 1 x 4 the length you want it to be - we usually cut ours about 3 ft long.

Next cut down the center - we call that ripping the board - except instead of cutting it straight we turn the saw on a 45 degree angle as shown in the illustration.

Next, pre-drill holes (through the center of the thickest parts of your boards) about every 8 inches.

Using a level, screw the thick side of one piece to your Upholstered Headboard or Legless Table and with the angle pointing down. (This creates a small channel between the thin angle and the headboard).  

Find your studs - this is a must - you gotta hit a stud on at least 2 holes.  The more the better.  

Then install one screw into the thick side of your remaining board to the wall (into a stud) with the angle pointing up. (this creates a space between the thin angle of your board and the wall.  Use a level and make sure the board is perfectly level.  After doing so, install the rest of the screws.

We apply little spacer blocks from the left over 1 x 4 at both bottom corners of the headboard to keep it from tilting.

The boards are really inexpensive BUT - if you don't have access to a saw or don't feel comfortable using power tools you can cheat.  I sometimes use a couple of the Rubbermaid FastTrack Shelving Rails.  
These are sometimes hard to find because they have changed the design over the years.  They have to look exactly like this so that they hold your piece really close to the wall
 Your local hardware stores should stills stock them.  

That's it !!!