The public school would be required to meet some federal law, but not to provide your child with a FAPE, under IDEA.
The public school would not be required to provide the homeschooled child with all the services mandated under IDEA (including providing FAPE or fulfilling an IEP), because those requirements apply only to public school students. A homeschooled student attending class or participating in a public school activity is not a public school student.
However, the public school would be required to provide the services required by Section 504 of the Americans With Disabilities Act, which gives certain specific protections to every person with a disability in any program or activity that receives federal funds.