Right off the bat, two lines look quite wrong. The "second stage", where you read from the file, should look like

    $visites = <hits>;
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That's how you read from a file. The sixth stage, where you close the file, should look like

    close hits;
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In addition, though, you should be:

• Checking for errors on filesystem calls (like open and close).
• Performing some sort of file locking.
• Turning warnings on (#!/usr/local/bin/perl -w)
• Using strict:

      use strict;
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These are good practices for any programmer. The second, file locking, is especially important, because you could have more than one person updating your hit counter file at the same time. Thus you need file locking.

One of Randal Schwartz's Web Techniques columns focuses on file locking.