Repetition and practice are the main parts to learning any language, and French is a language that is commonly very poetic in nature as it is a romance language. You can find a tune to match the numbers to or simply use it in place of English numbers for practice.
French can be a difficult language to learn to count in due to the fact there is eventual math use. However, we learn to count in any language the same way we learned to count in our first. Detecting patterns is good practice; if you can remember the first 16, and the first number that begins each group of 10, it becomes easier to understand and follow the way it's set up. For example, similarly to English, where we would say fifty-seven, it would be cinqante-sept (50-7).
However, this is not usable for all of French, as certain numbers require addition, like eighty, which is quatre-vingt in French, or 4 20s. Learning to count in any language is a matter of practicing until it's stuck in your head, and using it as often as possible to count things in your daily life until it becomes as second nature as your native tongue.