Reverse Proxy To Cloudfront CDN

We want to forward all requests to domain.com/foo to a S3 Bucket fronted by Cloudfront. The idea being that our domain is used while the content is loaded from S3/Cloudfront. I have Apache setup to reverse proxy requests to /foo thusly:

<Location /foo>
    RequestHeader set X-Forwarded-Proto "https"

    ProxyPassReverseCookiePath / /foo

    ProxyPass http://bar.cloudfront.net/
    ProxyPassReverse http://bar.cloudfront.net/
</Location>

However when I hit domain.com/foo I get a 403 Forbidden from Cloudfront.

I tried adding the header RequestHeader set Host "bar.cloudfront.net", the page loads and I see the content in the s3 bucket, but then the domain is obviously the CDN domain.

Update:

I swapped out the cloudfront URL in the Apache config for the s3 bucket's public URL and it worked, while preserving the hostname. So I believe this confirms its an issue with Cloudfront.

I added our domain name as a CNAME on CloudFront. Then set the RequestHeader set Host to our domain name with the /foo. This preserves the host name but causes a 400 error from CloudFront.