Jalima You do need travel insurance if travelling in France. Your EHIC only pays part of your costs.
The French health system is a combined private/public system. French people, unless very poor are expected to have compulsory private health insurance. The state covers part of the cost, the insurance the balance. The EHIC covers the state contribution . You need an insurance policy to cover you for the balance of the costs.
When DH was taken ill and needed to be seen in A&E, we got a bill for about 32 euros, plus the cost of the drugs he was prescribed. Another 40 euros.
We use the free travel insurance provided by our bank and DH pays a £90 supplement for his pre-existing conditions (diabetes and high blood pressure). That is £90 a year as we have an annual travel policy.