As already covered Reflex, Will, and Fortitude model actual actions, which breaks down quite quickly in abstracted combat (if you duck out of the way of the fireball using reflex, how come you're not prone?). So if you're going to use a modern system and want it to have some old school style and flavor, you'll need a replacement. Here's my suggestion.
Obstinance: For saves versus things that affect the body and soul. Use this for poison, death magic effects, paralyzing and effects that attempt to override your mind. Also can be used to resist petrification effects. Modified by Constitution for physical and Wisdom for Mental results. (You may allow these modifiers for only certain races or classes for an even more old school feel.)
Chicanery: For saves versus devices, traps, and short confidence games. Use this for dodging out of the way of a trap, for a magic user firing a bolt or beam from a device, or for when people are trying to charm, apologize or fast talk you into doing something you don't like. Also can be used to resist polymorph effects. Modified by Dexterity for the physical effects or Intelligence for the mental ones. (You may allow these modifiers for only certain races or classes for an even more old school feel)
Destiny: For saves versus area affects, anything to do with luck, and a general magic save versus spell effects. Use this for when you set off a trap that ignites a flaming cloud, when a dragon breathes, or on any spell or effect that doesn't match one of the above saves. Modified by Charisma usually, but can use any appropriate stat for the specific save. (You may allow these modifiers for only certain races or classes for an even more old school feel)
Remember, that these saves are abstract, so the specific manner in which the damage is avoided is up in the air (and should directly impact play).
Obstinance maps to Fortitude, Chicanery to Reflex, and Destiny to Will for advancement as good or bad saves. The easiest way to handle modifiers is to not give them out at all (making it more dangerous) unless you have a special case, and then only for a specific effect. i.e. The same as it is handled in 1st edition - where your Paralyzation / Poison / Death magic save is a flat number, and Dwarves get +4 versus poison on their saves. Just write out the granted modifier next to the save.
I only do this because I loath the 3e save system, and it appears that it is retained in the DCC RPG. I give them permission to freely use this system in their project.