It is correct, and cannot be replaced by the word 'free'.

The way you are stating it is certainly correct and the tone is appropriate if you mean for it to be formal. You might hear something like "once you're free" or "whenever you're free" in informal discourse in this context if it was about a meeting in person or a phone call. But in the context of expecting a written reply, the informal way to say it would more likely be something like "when you get a chance."

"Please reply at your earliest convenience. I look forward to speaking with you further.", would be a native English flow. I hope this helps. The original would be difficult for an American to understand but you're doing great with choosing good vocabulary :) The vocab would just have to be used a little differently. I wish I had time to explain the grammar now but feel free to use my example for the email or formal letter you need to send :) I would be happy to help you with your grammar and writing in my writing class. I am an Editor-in-Chief :) Have a wonderful day and keep writing! :) Sincerely, Ana :)

I think it is perfectly used. Well done