Learn French: L'agriculteur travaille dans les champs.

While a field is flat ground, French treats it as an enclosed area or environment, so you use dans (in). English also says 'in the fields', so this is a direct match, but learners often mistakenly guess sur (on) because they think of a flat surface.

What is the difference between un agriculteur and un fermier?

Agriculteur is the modern, professional term for a farmer (someone who works in agriculture). Fermier is also common but traditionally refers to someone who rents the land they farm, or someone who runs a farm with animals (une ferme). In news or official contexts, agriculteur is preferred.

Are the consonants at the end of champs silent?

Yes, both the p and the s are completely silent. The word is pronounced exactly like chant (song), using just the 'sh' sound followed by the nasal vowel 'an'.

I know the word champ means 'field', but are there any common idioms that use it?

Yes! A great expression to know at B1 level is sur-le-champ, which means 'immediately' or 'right away' (literally: 'on the field'). You will also see it in the famous Parisian avenue, les Champs-Élysées (the Elysian Fields).