With a diesel engine you could fuel it with biodiesel made from cooking oil, sodium hydroxide(an impure solution likely sufficient for our purposes could be obtained from wood ash, this was normally used in soap making) and methanol(obtainable by distillation and used as early as ancient egypt)
Also certain non diesel engines can run on ethanol, including some motorcycles made for brasilian market that can run on E100 that is 94.7% ethanol (rest is water) so fuel for that engine could be distilled with medieval technology