I have that too - too much rain - I think it's a fungus called Alternaria zinnia.

I removed the bad leaves and sprayed with a baking soda/vegetable oil/castile soap solution (2T, 1T, 1/2T) in a gallon of water. Used a gallon sprayer and sprayed the lower half and mulch around the plants. Hoping it helps.

Here is a link that might be useful: Zinnia Diseases

where do you get Castile soap?
What do you mean a 'gallon sprayer' ?

Castile soap is often available at Dollar Stores or Big Box stores. It is old fashioned bath soap. Inexpensive, usually.

A Gallon Sprayer is a pump up type that you can mix chemicals or organic concoctions in and spray on your plants. Look in the garden section of a Big Box Store. They are usually around $10. They are a good tool to have if you are serious about gardening.