Do I need to contact professors before sending my postdoc applications? I intend to apply for a call for a postdoctoral position. Is it necessary to contact professors before sending my application formally? If so, which documents should be sent? Is my CV enough or should I also send a research statement?

My field is mathematics and I am applying to positions in France and Italy.
It's unclear if you mean cold-emailing professors for positions, or if you're planning to utilize the network that you've built from publishing and attending conferences.

I would highly recommend emailing other academics you've meet a conference that are already familiar with your work and letting them recommend postdocs to you.

Cold-emailing is unlikely to help much as professors are inundated with emails from prospective students who want a leg-up on acceptance, and your email is likely to get lost in the clutter.

EDIT:

The last sentence was unclear.  By cold-emailing, I meant looking up the email of the hiring manager/professor for the postdoc and sending them a follow-up email.

Most professors receive HUNDREDS of legitimate emails every day from the students they teach and advise, journal/conference submission request, other professors, or their side consulting business.  A "cold-email" is likely to get relegated to the spam box.