I don't know about common but certainly not uncommon--had several friends that did.
It will help a bit if there is some small connection (e.g. your current advisor and new one, a collaborator even once removed, previous members of lab group, etc.). After all any time you hire someone this can be helpful. But maybe even a little more when you are bringing someone in from overseas.
Of course, many people still come/go based on blind opportunities (replying to posted positions) so go ahead and apply for them.
In addition, I urge to pro-actively reach out to some people in the field that you would like to work with. When doing so, find some potential points of commonality other than just "I want a gig--got one?". Something along of the lines of
"Professor Francais, I wanted to reach out and introduce myself.
I noticed that you are one of the few French researchers in density functional theory for industrial materials. I am very interested in moving into this topic. (Have worked previously in an analagous but different area: Hartree Fock calculations of pharmaceutical materials.)
In addition, I would find it a pleasure to experience France at your institute on the banks of the Seine.
Do you have any current positions open or do you foresee any coming open? Could we have a conversation about your research?
Sincerely, O. Bektas
You will need to figure out the visa situation when things get serious but I don't think Turkish citizen (guessing based on your profile) will be hard for a temp science position in EU.