I'm hoping there is a regular shuttle service which is easy to find and fairly cheap.
If you want direct, then there’s no direct rail option, but there’s a direct bus line, aptly named “Le Bus Direct”.
If you want rail, then there is no direct service. The easiest option is RER B to Gare du Nord then RER D to Gare de Lyon (same platform transfer in Gare du Nord).
From the Airport you first catch the B line train to Chatelet – Les Halles, before then changing to the A line to Gare de Lyon. The whole journey takes no more than 45 minutes, and you will be able to catch the B line every 10-15 minutes. A single for the journey is about $10. There's huge signs around the airport that point you in the right direction, and you can buy tickets from many different machines that take both card and cash.
Alternatively there are options by bus, with at least one direct route, this takes over an hour though and costs around $17.