What if I add cloves to French Onion soup?

It will ruin the soup only if you or those to whom it's served don't like a taste of cloves.
There ARE recipes for French Onion soup that include cloves, so using them isn't (totally) beyond the pale, but it sounds strange.
Maybe make some Indian soups, or recipes which more commonly feature cloves.

Yuck. Don't do it.

It's your soup, put in whatever you like, but I don't think you could reasonably call it French Onion Soup with cloves in it.

I love cloves but not in French Onion soup. Yes, it would change the flavor. If you, personally, would like cloves add a dash (or a dried clove) to your soup bowl.

Personally, I do not like that flavor but I think it would overwhelm the dish.