When going out for dinner or lunch, is it rude/odd/impolite/cheap/etc to only order a “plat principal” (not counting a beverage) Or is it proper to order with at least an entree or desert?
Not rude, not cheap. If all you want is a main dish and a beverage, that's perfectly fine.
We just came in from a dinner with friends. My husband had a main and a glass of wine. I had a first course and a glass of wine, no main course. No desserts. No problem.
One thing that is somewhat frown on is ordering a main and splitting it. One of us orders the salad and other the main and quietly share.
One way to avoid any issues is to eat in cafes and bar/bistro joints where you can sit at a table and drink, with or without food, and they don't care anything about each person ordering 2 or 3 courses like more traditional restaurants with a single evening seating.
I had no problem ordering an appetizer (entree) or a main (plat) or two appetizers. You can often get a good deal with a "formule" that consists of entree+plat or plat+dessert for a relatively good price, but there's nothing "proper" involved.
In France I never feel shamed when I don't order alcohol - unlike here in the US when you feel that your server gives up on you and your quality of service diminishes.
You can request tap water -- "d'eau ordinaire" -- and the cover charge, if any, will be small. I like fizzy water, for a special touch to the meal, and am willing to pay for it accepting that the restaurant is making a small profit.
You can request tap water -- "d'eau ordinaire" -- and the cover charge, if any, will be small.
Slight correction if I may: there are no cover charges in France, and tap water is "une carafe d'eau".