IMO you'd be nuts to travel without travel insurance. The E111 might get you hospital treatment but it isn't going to get you transported home if you have a serious injury or major illness that requires specialist transport home and stuff like that.
To give you some idea of costs to be got home from France after an accident, my travel insurance covered the following to get me home last April:
Taxi to airport 297 euros
3 seats on the plane, so I could keep leg straight.
7 seat taxi from stansted to home. (£100?)
Doctors bill, 200 euro.
Pharmacy bill 150 euro.
Also they set everything up after 1 phone call from me, and paid all bills direct.
Won't leave the country without decent insurance, all an E111 could do is save you your excess.