Timing can greatly affect lodging costs. I suspect treemoss's estimate might work for a November trip, but I wouldn't count on it for May unless you will accept quite basic accommodations (which might mean no elevator, etc.). Lodging will be a large portion of your costs. You really need to do the suggested research on a website like booking.com.
Hotel costs for the best-value places tend to creep up as the arrival date approaches, so if your trip is many months in the future, be aware that the rates you see today may not be available a month of two from now.
It's easier to control food expenses by shopping in supermarkets or street-food stands for a lot of meals (if you need to pinch pennies). I like to include some protein at breakfast time, so I watch for bakeries that have little mini-quiches for sale. I don't know the going price in Paris, but I've paid less than 5 euros for a filling quiche in Lille and Arras. Crepe stands will cost you more, but they are a very good option if you don't need a sit-down meal.
On weekdays, many French restaurants have special deals on multi-course lunches, so eating your main meal at lunch rather than dinner can save quite a lot of money. That means being willing to take a break from sightseeing in the middle of the day, but it sounds as if that might work well for you.