Presuming you don't need to handle escapes (e.g. the closing quote character never will appear inside) you (probably) can get away with something simple along these lines (writing as a script for clarity; reducing it to perl -lnE left as an exercise):

use utf8;
while( <> ) {
  chomp;
  my( $leader, $fields ) = m{\A (.*?) « \s* (.*?) \s* » \z}x;
  my @items = split( /\s+/, $fields );
  say qq{$leader « }, join( q{,}, @items ), q{ »};
}
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Edit: Tweaked the output, as you do have a couple spaces still in your output as hippo points out. One presumes you mean to canonicalise to pad with a single space around the joined items, but . . .