I suggest you run your RTC on GMT (aka UTC, if you’re French). If you’re just using it for data logging or the like you can probably run entirely in GMT. If you want to display it to a user you probably want to do that in localtime. The ESP8266 C API doesn’t have support for timezones, so you’ll need to add your own. Adding or subtracting a few hours is easy enough, but applying daylight savings time (DST) during the summer is a little more tricky. A quick google search found a few examples but they all assumed the adjustment happened at midnight, so I’ve created an extended version that changes at 2am, as happen here in the UK. This is an example and will need to be modified if you’re not in the UK. Ideally the function would parse a string with timezone specific definitions rather than having hard coded rules, if you want to do this hopefully this code will serve as a starting point.
Code now on GitHub: https://github.com/raburton/esp8266