Slice the french bread into 1 - 1.5 inch slices. If it's fresh bread, I recommend toasting in a toaster. No need to get any coloring, just for a few seconds to help absorb the egg mixture better and for a crisper texture.
In a medium bowl, whisk the eggs, half-and-half, milk, sugar, yogurt, vanilla extract, salt, and food coloring together until combined. Use a hand blender or an immersion blender to get the job done quicker and to remove the yogurt lumps. The mixture will be thick and creamy. *Make ahead: at this point, you can cover the mixture up and refrigerate until the morning when you are ready to make french toast.*

Soak the bread slices in the mixture for about 1 minute on each side. Meanwhile, over medium-low heat, melt 1 Tablespoon of butter + 1 teaspoon oil in a skillet pan. Place 2 slices into the pan and cook until gold brown on each side, about 3 - 4 minutes on each side. Melt more butter + oil in skillet pan for the next batch. Serve immediately.