WebSocket Server for MKR1000
This old and simple one has always worked for me on several Arduinos (but I haven't tried it on the MKR1000 specifically):
https://github.com/morrissinger/ESP8266-Websocket
I have forked it and made some changes, but nothing fundamental:
https://github.com/ocrdu/NINA-Websocket
Have a go, it just might work for you.