This version uses fewer lines, and is slightly quicker for me:

function($fileName)
{
    $handle = fopen($fileName, 'r');
    $attributes = fgetcsv($handle);
    for($i = 0; $line = fgetcsv($handle); $i++)
    {
        foreach($attributes as $attribute)
        {
            $lines[$i][$attribute] = $line[$i];
        }
    }
    return $lines;
}

This version uses fewer lines, and is slightly quicker for me:

function($fileName)
{
    $handle = fopen($fileName, 'r');
    $attributes = fgetcsv($handle);
    for($i = 0; $line = fgetcsv($handle); $i++)
    {
        foreach($attributes as $k => $attribute)
        {
            $lines[$i][$attribute] = $line[$k];
        }
    }
    return $lines;
}