What are good counter-top oven settings to reheat french fries soggy from refrigerating overnight?
They won't be as good as when fresh (of course) but generally:


You want the oven pretty hot. How hot depends on the oven, size of fry, etc., but a good first guess would be 425°F–450°F. On most toaster ovens I've seen, that'd be as hot as it goes. Let the oven preheat. Unfortunately, heating the oven is going to take longer than your five minutes, probably ten to fifteen... But as long as you stay nearby (just in case) you can do something else while its heating.
Spread the fries evenly on your piece of foil. Fold up the edges of the foil a little to keep them from sliding off when you move it. (Note: A plain, uncoated aluminum quarter sheet pan probably fits in your toaster oven, and can be had for under $10.)
They won't take long. Listen for them to start to sizzle. Once they've sizzled for a little bit (say, 30 seconds) pull them out and flip them. Put them back in and let them sizzle a little longer. Take them out, sample one, put back in if not done yet. I can't give you a time (other than "a few minutes") because it's going to vary a lot based on the fry, and even how much it has dried out in the fridge. Judge when they're ready based on the sound (sizzle), smell, color (browning), and taking one out and tasting it.


Notes:


You may find adding some salt helps them a lot. Same with some finely ground pepper. Or other powdered seasoning mixes like Old Bay.
If the center isn't warm enough by the time the outside is browning, use a lower temperature next time. If the center is overdone (e.g., dried out) before browning sets in, use a higher temperature.