To pass more than one css rule, but also a class, an id, or any html attribute to highlighted element, we can escape a quote to close the inline styling:
 ini_set('highlight.string', '#F8F8F8 ; font-size:1.4em\" class=\'string\' ');

To change the style directly from a CSS file, it is recommended to only go through classes instead of hard-coding it.
<?php
 $functions = array("default", "html", "keyword", "string", "comment");
 foreach ($functions as $value) {
 ini_set("highlight.$value", "highlight-$value;");
 }
?>

And in the CSS file (for example) :
.highlight-html { color: #000000; }
.highlight-default { color: #0000bb; }
.highlight-keyword { color: #007700; font-weight: bold; }
.highlight-string { color: #dd0000; }
.highlight-comment { color: #ff8000; }

*** Additions to the previous message ***
To change the style directly from a CSS file, it is recommended to only go through classes instead of hard-coding it.
<?php
 // Create an array with default php functions
 $functions = array("default", "html", "keyword", "string", "comment");
 // Replace color code (ex: #FF8000) with class name (ex:"highlight-comment")
 foreach ($functions as $value) {
 ini_set("highlight.$value", "highlight-$value;");
 }
 $content = highlight_file($filename, true);
 // or
 $content = highlight_string($string, true);
 // Convert style="color: highlight-function" into class="highlight-function" into $content
 // It allows you to modify only the default functions
 foreach ($functions as $value) {
 $content = preg_replace("/style=\"color: highlight-$value;\"/", "class=\"highlight-$value\"", $content);
 }
?>

And in the CSS file (for example) :
.highlight-html { color: #000000; }
.highlight-default { color: #0000bb; }
.highlight-keyword { color: #007700; font-weight: bold; }
.highlight-string { color: #dd0000; }
.highlight-comment { color: #ff8000; }