If I’m visiting the Schengen region, can I “work from home”?

I’m a US citizen. I want to spend about 6 weeks vacation visiting my friends in France, Spain and Italy. However, with taking this much consecutive time off from work my employer would require me to do daily check-ins (email and Skype).

It’s also very likely I would have to spend up to 20 hours per week fixing untoward problems. This would require me logging into my company laptop to write and submit code. Any hours that I spend doing company work I would be paid as a normal employee (vs. PTO for the rest of the vacation).

Is this legal as a tourist?