A glass of wine with lunch or dinner is normal. Drinking wine doesn't make you a tourist; chugging beer at noon does.
Ask for the 'vin de la maison' (house wine) — typically the best value. House wines are usually 4–8 euros a glass at bistros.
Don't refuse wine outright unless you have a reason; just sip slowly. Saying you don't drink because you're 'not driving' is meaningless in Paris where nobody drives.