Yours sounds like a very elaborate French onion soup recipe. Onion soup - at its simplest onions stewed in water - is an age-old food that nourished generations of peasants. In the last century, it became more refined and popular at bistros around Paris’ central market (Les Halles), when a bit of bread and cheese were added to the mix - although the soup was still made with water and not broth. Many versions have proliferated since then, of course, and most benefit from the richness of beef, chicken, or veal stock instead of water. We have not come across any recipe that calls for sauce diable.
Now to your question. A classic brown sauce diable is itself quite an underatking (requiring demi-glaze, which is another major production), and not at all worth the work to obtain 1 measly tablespoon.
A classic sauce diable calls for simmering a minced shallot, a cup of dry white wine, sprig of thyme, bay leaf, 1/2 teaspoon of dry mustard until reduced by three-fourths, then adding 2 tablespoons of tomato puree, 1-1/4 cups demi-glaze, a tablespoon of lemon juice, 1/2 teaspoon cracked black peppercorns and 1/4 teaspoon cayenne pepper, and simmering further until thickish. Strain the sauce, and add a tablespoon of minced parsley.
In your soup, the sauce is probably providing a little additional flavor depth. If you have a little demi-glaze sitting about, you could add that instead, or you could probably leave it out entirely.