After using a French press, you can properly dispose of coffee grounds by first allowing them to cool down to avoid burning yourself. Once cool, you can easily discard the coffee grounds in your compost bin, if you have one. Coffee grounds are a great addition to compost as they are rich in nitrogen and can help enrich the soil. If you don’t have a compost bin, you can also dispose of the coffee grounds in your regular trash. Just make sure to avoid pouring them down the sink, as they can clog the drains.