For a variety of relatively modern equipment, it would be possible to make fuel with Rennaissance level technology, specifically biodiesel. The chemical reaction to make this product takes alcohol and fat, usually vegetable oil).
Vegetable oil is trivial since it has been made in industrial quantities since prehistoric times. The distillation is trickier. The process was invented probably in the years BC with some sparse evidence from Hellenistic Greeks and India at that time. It was scientifically described by Arabs in the 9th century, used to produce pure compounds in Europe in the 13th, and producing large quantities of spirits in China by the 14th.
The problem is producing alcohol in sufficient quantity and purity to be able to create large amounts of fuel. That was only done in the 19th century. The combination of fractional distillation from Italy and mass production of China could possibly produce a large supply. In any case, it is barely plausible to create a fuel usable by modern tanks and armored vehicles.
A more plausible solution would actually be batteries. If there were a sudden leap in battery technology, such that you could charge up a tank and run it around a battlefield for a day or two on one battery pack, that would change things.
Electric power was not discovered in the Middle Ages, of course, but the engineering required to create large amounts of electricity would have been feasible using hydropower.
Watermills were well developed by the Middle Ages, especially in Europe. Metal mechanical parts were available for clocks by around 1300. Copper could be drawn and coated and then wound to create a dynamo. The combination of these things would make it possible to create an electric generation plant with 14th century technology, if only one had the plans to do it.
If some detailed instructions fell into the hands of a medieval genius, then it is plausible that an electrical dynamo could be created to charge battery powered modern weaponry.
One last note; the batteries themselves could not be of the chemical variety, since they would inevitably be dead after a few idle centuries. However, since these posited super-batteries do not exist, it is plausible to say that their energy density is some function of the physical structure at the molecular or atomic level; therefore, once they are recharged they will work just as well after a few hundred years in the ground.
Ammo vs Lasers
Obviously, finding ammunition for a war machine will be tough after some thousands of years. However, a directed energy weapon that does not need ammunition would be the way to go in this case.