France Insider is much more professional than the Connexion. More expensive I believe (no idea what the Connexion costs but can’t imagine it’s much - they certainly don’t pay for proper journalists,)
Or to go a bit wider you can get a paper/online subscription to a weekly magazine - huge number depending in your interests, such as Marianne or L’Obs for current affairs.
Or if you are in the South West this one might be worth a look?