You’d probably get a cock-eyed look if you tried to get tartar sauce for your fries at anyplace that wasn’t an English style Pub, here in Chicago. Of course most places with any kind of fish on the menu would probably have some and bring it to you, but it’d be pretty firmly entrenched in the goofy category.
Tartare is good when you’re having fish and chips. Gravy or tomato sauce (ketchup) are good for just chips by itself. Chips from fast food chains are good with sweet & sour. But for fries with anything else, bring on the American Mustard 
I’ll dip my fries in tartar sauce, malt vinegar, shrimp cocktail sauce, ketchup, mayo, ranch or blue cheese dressing, BBQ sauce, A-1 or Heinz 57 steak sauce, gravy, melted cheese and sometimes even mustard - but never any combinations of those (except maybe ketchup and BBQ sauce). One favorite of mine when I was younger and used to eat at Arby’s was their Horsey sauce (not made from horses).
I am a wild and free spirit and I won’t be pinned down to one fry dipping sauce.
Training Table fry sauce is made with approximately 2 parts mayo to 1 part bbq sauce. Theirs is outstanding–so is that found at Crown Burger and Hires.
mmmm . . . . fry sauce
I also like my fries with homemade mayo (not jarred–ugh), tartar sauce, salt & vinegar, thousand island.
And, speaking of thousand island dressing, it is divine with fried dill pickles.
I’ve found that the ideal combo at Arby’s is a mix of ketchup, Arby’s sauce, and their new Pepper sauce. A 2:2:1 mix is just about right.
Arby’s Horsey Sauce got me started on fries with horseradish. (And here I thought I was the only one…) That’s my favorite, although it’s hard to find. Otherwise it’s ketchup. Mayo is too bland for me. I’d probably be OK with what those westerners call fry sauce. One of my best friends is from Idaho and she brings it back to Ohio sometimes. Her favorite variation has ketchup, mayo, buttermilk and hot sauce.
GT