It is relatively broad consensus that Facebook is the most private directed of the social media. It is therefore quite normal to have a closed Facebook page, and this will not seem strange or suspicious. But Facebook is also by far the most widely used social media in Europe, and there may be something to be gained from using its network also there when applying for a job.
This can either be done by having a closed profile with a large network which also involves in job search, or you can have an open profile so recruiters or managers can become better acquainted with you.
If you choose to have an open Facebook profile, we recommend thinking through what you have lying there. You don’t need to be as professional as in LinkedIn, but Facebook may in fact be a good way to show a little "color". Don’t write anything you would not have been comfortable with saying in the canteen to colleagues, you don’t know well.
Not just be aware of yourself, think for a moment what your friends write on your wall, and the images they tags you in. All your friends are doing will not automatically reflect on you, but it helps to form an overall impression.