Does Arch Linux work on my i386 cpu. I read on its website that it's optimized for i686, does it mean Arch Linux won't work on i386. By the way, I don't want to compile it, I want to use the available binary if possible.
i386 is generally used to mean any 32 bit Intel CPU since the 80386. Seeing as how the 80386 went obsolete circa 1994 and nobody in their right mind still has one, most linux distributions these days compile their kernel with optimizations enabled that require the i686, or the pentium pro, and even that nobody in their right mind still has running.
So if you really still have an 18+ year old cpu, then no, it won't run.
Arch Linux uses i686-optimized packages which gives us improved performance over some of our i386-optimized cousins. This means that Arch Linux will only run on a Pentium II processor or higher. We try to stay fairly bleeding edge, and typically have the latest stable versions of software.
Linux kernel doesn't support the i386 architecture anymore. The support was dropped in 3.8 release, by the end of 2012. Therefore, you can't even compile it.
If you intend to run Linux on a processor that doesn't support the i686 instruction set, you are supposed to try old (and unsupported) versions of distros.
https://archlinux32.org currently deals with the old IA32 version of Archlinux. It has two brands, one called 'i686' requiring MMX, SSE and SSE2 for stuff like graphical interfaces and firefox (server stuff and text mode should work fine on at least CPUs supporting word-size NOPs for CET, in my tests as soon as a Pentium-S) and an experimental 'i486' one which currently runs in text mode only and with at least 64MB of RAM (via a special ISO or a PXE/NBD boot).
Old AMD (e. g. Geode) or Cyrix clones may lack too many features and may not work and require the i486 branch.
Graphic card support is hard since Xorg 1.20: Nvidia, AMD and Intel cards pretty much work fine. Also virtualized environments work like bochs-drm in libvirt/kvm. For other brands you are pretty much on your own.
The i486-branch is not for the faint-hearted casual Linux-user, more for enthusiasts. :-)