Teaching jobs in Cologne or surrounding aread

Hi there, my name is Sam and I am looking to move to Germany in October (2017) to start my graduate school program. My girlfriend will be coming along for the journey and is looking for employment in or around the same area that I am going to school at (Univ. of Cologne) She is an elementary school teacher and art teacher here in California with some some experience in private school settings. Does anybody have any ideas of where to start looking for teaching jobs? She is looking to get a certificate to teach English abroad but even those jobs can be harder to find. I just feel that schools in Germany have to be looking for American teachers speaking English to teach kids. If you have any ideas, connections, or know of somebody or a school looking please let me know as soon as possible.

There are a lot of public schools that she could contact. I am sure they'd value a native speaking English teacher (although she'd compete with British nationals here, who have to be preferentially hired as long as they're still part of the EU). Precondition is an educational university degree and fluency in German.
If she doesn't speak German, she'll have problems finding any job (only international schools might be an option).

Thanks for the info, and heads up about the U.K. Folks I hadn't even really considered that.