In my F-Type V6 AWD 2017, the start/stop is no more effective. During the stop the engine does not swich off anymore. May be I need a new battery?

 

Can be and you can have it tested by checking not just voltage but more imprtantly cold cranking amps. Also not all eco issues are battery many are software and modules

 

For the first few model years, a 2nd smaller lead-acid battery was used for Start/Stop. That battery was removed in later years - my assumption is they switched to an 'ultracapacitor', which is what many car manufacturers use for start/stop. Could be that, or as Brutal says, other software or modules.

Or your battery. If the voltage is too low, start/stop is disabled.