I have an older laptop with 1GB graphics and 2.3 GHz i5 processor. Does anyone have any ideas on how to improve FPS in F1 games so that playing at 30/40 FPS would be possible? Would only be something unique so buying a new graphics card would not be an option for me.
Try to debloat your Windows (if you use Windows).
There are some videos on the net, I think "Windows 10 Debloater" and the "TGF Tuning Pack" are good.
These tools remove unnecessary processes in the background and may give you better performance.
Take a look at "TGF Tuning Pack" on YouTube, there's a presentation and instructions of the program directly from "The Geek Freak".