To be 'sick of something' can only be negative. It means that you have done - or been exposed to - something so much that you can't take any more. You are now thoroughly bored with it.

Another idiom with a similar meaning is 'fed up with'. If you're sick of French or fed up with learning French, you're tired of it and don't want to do it any more.

Both phrases might suggest a feeling of nausea from overeating.

"I'm sick of French" means "I don't want to learn French anymore."

You could also say:

"I'm tired of French"

"I'm bored with French"

More informal / slang could be:

"I'm over French" or "I'm *so over French"

Hi

I am sick and tired of something means you can't stand it anymore!