Products bearing UL/CSA approval don't automatically give you the right to affix the CE marking. The reason for that is in the technical file's requirements. If you want to know whether the existing UL/CSA files may be used for proving CE compliance of your product, you will need to go through a brief documentation review with a CE expert.
However, please note that the CE marking process might be facilitated by letting you skip (parts of) the expensive product compliance testing if your product has already been UL/CSA certified. That can happen only in cases when the UL/CSA testing and certification have been conducted in accordance to international standards similar to the European harmonised standards.