In France there is a sharp distinction between a tax and a mandatory contribution to the social security system. Mandatory contributions (cotisations sociales) are withheld from your income and go to a bunch of ad hoc institutions managing the social security system (health insurance, retirement, unemployment benefits, etc.). Taxes, including income tax, are paid directly to the tax office (although there is a plan to have employers withhold them in the near future) and go to the state's budget. Work contracts and collective bargaining agreements always refer to the gross income, before paying the mandatory contributions.
So if 20,000 is the gross figure, you first need to use one of the many salaire net/salaire brut calculators you can find online. This will take care of the social security side of things. The amount left after paying that is what will be transferred to your bank account every month. It hasn't been taxed yet. What you have to do is plug this net income figure in an income tax simulator and make sure you keep that money to pay the taxes when they are due (you can ask the task office to make a monthly bank transfer but I don't think that's possible if you have never worked in France before).
There can still be some small payments for other things and some subtleties around how the CSG/CRDS interact with the income tax but it should give you a good idea of your actual income.
Furthermore, there is no "renter's tax" but a "taxe d'habitation" that everyone has to pay for their main residence (whether you own it, rent it or even live in it without paying anything). That's not directly related to your income and it does not really make sense to consider it in that way, it's more something to include as part of the costs of accommodation (along with utility bills, etc.), a bit like VAT is part of the costs of grocery shopping. This tax is being phased out but you will still have to pay most of it for 2018. The rates and amounts depends on where you live.