Hey ​@Attila Simon Paul here from Intercom support team :D 

Unfortunately, Intercom does not currently support hosting the Help Center on a custom subpath (like www.oursite.com/help). It only supports custom subdomains (e.g., help.oursite.com).

Why!? Intercom’s Help Center is hosted on its own infrastructure and relies on CNAME records and SSL handling that can’t operate properly behind a path (like /help) on your main domain. So even with the correct DNS setup, you'll get a “Not found” error if you try to use a subpath.

Well, that's not want the intercom web site and FinAI says. They both say it should work.

Also, this is a much more simple feature than a subdomain, as there is literally no setting required for it, as the setting is to be made on the origin site in form of a reverse proxy setting, and intercom should just allow it by checking the custom URL setting.

Also, to explain why would someone need a subpath instead of a subdomain: 

The rich textual content added to a Help Center contributes significantly to the SEO score of a web site. If  help center is available at an intercom domain, or a subdomain of our web site, this SEO effect for the main domain is ZERO (or actually even negative if we (re)move the help content from our current site to the intercom help center),

The only case, which helps to maintain / improve the SEO of our main site is if the help center content is available on the same URL as our main site.

This is why we must have the help center set up as a subpath of our main domain. Please make it work ASAP.

1. Check Articles: Ensure you have at least one published article in Articles > All Articles.
2. Verify Intercom Settings: Go to Settings > Help Center > Domains, add www.oursite.com/help, and click Save and Set Live.
3. Configure DNS/CDN: Set a CNAME record (www → custom.intercom.help) and route the subpath (/help) to Intercom via your CDN (e.g., Cloudflare Page Rules). Ensure SSL is set to “Full.” 
4. Test: Clear your cache and visit www.oursite.com/help.

Could you confirm if you have published articles and your DNS provider?

Adding a CNAME for www pointing to Intercom will override the entire site, not just the /help subpath. This is clearly not the solution.

I spent some time reading into this for you Simon.. You can only reliably set up a custom subpath for your Intercom Help Center using AWS CloudFront or a similar CDN with path-based routing. Cloudflare does not support this for most users. The "Not found" error is due to missing or incorrect routing for the subpath. For most setups, Intercom recommends using a subdomain instead.