In the Prestashop backend I activated the webservice and I created an authentication key. Testing in browser works well but now I want to access the webservice via JavaScrip
Although i am not php guy and i haven not used prestashop ever, but may be you forgot provide access in your crodova application this might be the issue please add
this to your config.xml file hopefully it will work thanks, please do not forgot mark as an answer if it helps you..