Pull up and destroy any basil plants you suspect of being infected with Fusarium as leaving the plants is place will only perpetuate the disease life cycle in the soil.
Pull and destroy all weeds from the area around the infected soil as some weed species can hold the fungi and exacerbate or perpetuate the infection.
Plant Fusarium-resistant varieties of basil if you are trying to grow the herb in the same soil location. Plant basil seeds of the Nufar, Aroma 1 or Aroma 2 varieties as these are known to be fragrant but still resistant to the disease.
Refrain from planting any Fusarium-susceptible plants -- such as tomatoes, potatoes, eggplant or peppers -- in the infected soil for roughly 7 years as they will fall prey to the same fate.
Relocate your new non-Fusarium resistant varieties of basil plants to another location on your property well away from the area with soil you now know to be infected with Fusarium.