French Free Artillery Rule

We always assumed the French got one free artillery piece that has to be the same as the one you pay the points for. Someone just pointed out the rule say, “French Armies get one free Inexperienced or Regular artillery unit. This unit can be any anti-tank gun or field artillery piece in the French Army list (except for Heavy Artillery). This unit is in addition to the number of artillery units normally available.” It really doesn’t say you have to pay the points for one to get a second. Does that sound right? Maybe we confused the free French Inexperienced squad that must be identical to the cheapest one already purchased and assumed it applied to the artillery piece too.