Preheat grill pan, nonstick griddle, large nonstick skillet or table top electric grill to medium high heat.
Add 2 tablespoons of oil and Canadian bacon. Warm bacon and caramelize it at edges, 1 to 2 minutes on each side. Remove to a piece of foil. Fold foil over loosely to keep warm.
Combine chicken, paprika, poultry seasoning, grill seasoning, shallot. Score meat with the side of your hand to separate into 4 equal amounts. Make 4 large patties, 3/4 to 1 inch thick. Drizzle patties with oil and place on hot grill pan, griddle or in skillet. Cook 5 minutes on each side, until chicken is cooked through.
Top patties with reserved cooked Canadian bacon and Swiss cheese. Fold each slice of cheese in half to fit the burger. Cover loosely with tin foil. Turn off pan and let cheese melt, 2 minutes.
Combine mayonnaise, mustard, tarragon. Slather bun tops or English tops with sauce. Place Cordon Bleu burgers on bun bottoms and top with lettuce and tomato. Put bun or muffin tops in place. Serve with oven fries.