Learn French: Les piétons évitant la circulation sont prudents. - The pedestrians avoiding the traffic are careful.

Yes! Les piétons évitant la circulation... means the exact same thing as Les piétons qui évitent la circulation... (The pedestrians who avoid the traffic...). Using the present participle (-ant) is just a slightly more formal or concise way to replace a qui relative clause.

Why doesn't évitant have an -s at the end to agree with the plural les piétons?

When a present participle replaces a relative clause (showing an action the noun is doing), it acts as a verb and never changes its ending. It only gets an -e or -s when used purely as an adjective to describe a quality. Because the pedestrians are actively avoiding the traffic here, évitant stays invariable.

Since évitant doesn't agree with les piétons, why does prudents have an -s?

Because prudents is a standard adjective, and adjectives always agree in gender and number with the noun they describe (the plural les piétons). Évitant is a present participle acting as a verb, which is why it gets an exemption from this rule!

Why use la circulation for "traffic" instead of le trafic?