When you have the Cloudflare CDN in front of your website it serves static resources without hitting the main web server. With page rules you can also tell it to cache html and serve that directly. In that case you could have 1000 visitors served with only one hit to your web server, so your server logs will show much reduced traffic.

I know you can get a look at the stats around pages and hits on the control panel, but does CF let you get access to something similar to apache logs so you can get proper traffic figures and do analysis of visitors?

I'm on the free plan.