"If my packet in vrf RED at CE Router, goes to the vrf GREEN configured at the PE Router, what will be the packet flow?"
If would be a packet flowing from your CE Router's RED VRF to your PE Router's GREEN VRF. I.e. your packet flow is actually described in your question.
If your more familiar with L2, consider having two VLANs 2 and 3, which we'll also name the RED and GREEN VLANs. (BTW, Cisco's VRF-lite is built upon VLANs, so this analogy might be a bit closer to reality than you might first assume.)
How would packets move between these two VLANs? (Generally via L3.)
What happens if you interconnect a switch with a VLAN 2 access port to another switch's VLAN 3 access port? (Frame/packets will flow across the two ports, although if you use locally configured MACs on both VLANs, which overlap in assignment, you'll [likely] have undesired results,)
Just interconnecting two devices within different VRFs will allow packets to flow but since VRFs are L3, you might have routing issues, as likely the two VRFs don't know of the other VRF's addresses nor likely will they being sharing a dynamic routing protocol. Further, IP addresses might overlap too.
To properly share packets between VRFs, you need to deal with all the possible L3 issues, again, much like interconnecting VLANs.
I suspect there's some concept about VRFs, which is unclear, which might be because you believe it more complex than it is.
VRF, implementation, though, can get complex, just as "ordinary" L3 routing might too.
