If you are resident in France in a given tax (i.e. calendar) year, then you must report all worldwide income. There are a number of devices in place to avoid double taxation of income coming from outside France. But initially, all your worldwide income is considered in order to determine your tax bracket.
For some income, if there is a tax treaty between France and India, you are granted a tax credit equal to the French tax on the income. For other income, you receive a credit for tax you have paid elsewhere on the income.
France apparently does compare tax returns with various countries with which they have tax treaties, though I don't know much about just how and how often this is done. I have also been told that when a foreigner dies in France, their tax records may be exchanged with their home country in order to find various accounts that may not have been declared properly - whether in France or in the home country. This obviously may not affect you, but I know of a few heirs who were pretty upset when the French government wound up seizing undeclared foreign accounts.