YOURTHEME.theme.php

<?php

/**
 * Implements hook_preprocess_HOOK()
 */
function YOURTHEME_preprocess_paragraph(&$variables) {
  // Populate color templates vars, based on chosen color.
  $paragraph = $variables['paragraph'];
  if(!empty($paragraph->field_bg_color)) {
    $bg_color = $paragraph->field_bg_color->color;
    if (!empty($bg_color)) {
      $variables['bg_color'] = _get_color_class_suffix($bg_color);
    }
  }
  if(!empty($paragraph->field_text_color)) {
    $text_color = $paragraph->field_text_color->color;
    if (!empty($text_color)) {
      $variables['text_color'] = _get_color_class_suffix($text_color);
    }
  }
}

/**
 * Helper function to provide usable classes,
 * transformed from html color codes provided by 'field_color' module .
 * @param $color_code
 * @return string
 */
function _get_color_class_suffix($color_code){
  switch ($color_code) {
    case '#333333':
      $color_class_suffix = 'dark-grey';
      break;
    case '#F9F9F9':
      $color_class_suffix = 'light-grey';
      break;
    case '#E8AD00':
      $color_class_suffix = 'dark-yellow';
      break;
    case '#5C2483':
      $color_class_suffix = 'dark-purple';
      break;
    case '#EA560D':
      $color_class_suffix = 'dark-orange';
      break;
    case '#404D23':
      $color_class_suffix = 'dark-green';
      break;
    case '#96A499':
      $color_class_suffix = 'light-green';
      break;
    case '#FFFFFF':
    default:
      $color_class_suffix = 'white';
      break;
  }
  return $color_class_suffix;
}