There's enough up there about the correct use of glob() and of m{}.

I'd like to point out it's silly to glob on *.* and then ignore anything not matching *.c. Be more specific in the glob and you won't need the internal condition:

use 5.010;
say for glob '*.c';

# or if you're doing more than using the filename once .. 

for my $file ( glob '*.c' ) {
    print $file, "\n";
    lots_of_complicated_code( $file );
}
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To get an array of filenames, see open, opendir Duh! Sorry, readdir, or any number of threads here (hint: Super Search with terms like "dir files" or similar).

Of course, you could make your list with

ls -la /dirpath/dir/ > file_of_names
    or
dir /a /dirpath/dir/ > file_of_names

Moving on, your regex would (if the script worked) catch files with names like pqr.cobol so you might consider this:

#!/usr/bin/perl
use Modern::Perl;
use Diagnostics;

my (@file, $file, $filename);

@file = <DATA>;

for $file (@file) {
    if($file =~ /\.c$/i) { # match only filenames ending in ".c" or ".
+C"
        $filename = $file;     
        print "$filename\n";            
    }
}

__DATA__
bzz.c
bzz.doc
pqr.cobol
xyd.foo
123.1c
def.C
foo.endswithC
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For the record, though, your regex does achieve a good many proper exclusions

bzz.doc             \
123.1c               # not matched by your regex, ++
foo.endswithC /

Angle_brackets don't work that way.

They do.

perldoc -f glob
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++ for your reply, JavaFan because I was misreading this (from the glob doc you cited):

Note that "glob" splits its arguments on whitespace and treats
each segment as separate pattern. As such, "glob("*.c *.h")"
matches all files with a .c or .h extension. The expression
"glob(".* *")" matchs all files in the current working
directory.
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Nothing there bars this:

#!/usr/bin/perl
use Modern::Perl;

my @arr = glob("*.*");

for my $line(@arr) {
    say $line;
}
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Also, as noted by Corion, perlop is relevant.

If what the angle brackets contain is a simple scalar variable (e.g., 
+<$foo>), then that variable contains the name of the filehandle to in
+put from, or its typeglob, or a reference to the same. For example:

    $fh = \*STDIN;
    $line = <$fh>;

If what's within the angle brackets is neither a filehandle nor a simp
+le scalar variable containing a filehandle name, typeglob, or typeglo
+b reference, it is interpreted as a filename pattern to be globbed, a
+nd either a list of filenames or the next filename in the list is ret
+urned, depending on context.
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Above blockquote added as an update, for future readers

TY, both!

You could use glob to get the file names. Something like

for my $file (glob('*')) {
#....do stuff
}
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But do check the help first, glob takes a file match pattern NOT a regex :)

use File::Glob ();
foreach $file (glob('*.*')) {
    if ($file =~ /\.c/) {
        $filename = $file;
        print /$filename\n/;
    }
}
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The way that I routinely deal with things like this is to use File::Find, or File::Find::Object, or any one of their many brethren.

Basically, my thought is, a very complete and well thought out solution to this very well-known task is at my fingertips, so I’m gonna grab it and use it and move on.   I encourage you to do likewise.

Also, and on a more general level, sometimes file-searches will be disrupted by things that you do to those files or to the filesystem within that loop.   This seems to be particularly true in Microsoft Windows.   Therefore, my customary approach is to build the list-of-files first, explicitly close the search, and then to go back and process that list.   The exact details depending upon the number of files that I expect to see.