Is it permissible for a resident of France, for whom the nearest mosque is 8-9 km away, to pray Dhuhr at home as a present (not qada') prayer when he is exhausted from his night work, or is the Friday prayer obligatory for him at the mosque?

The general rule is the obligation to strive to attend Jumu'ah prayer, even if the distance is far, as long as there is a mosque in the city. However, if overcome by sleepiness or if there is difficulty in going, this is considered an excuse that drops the obligation of Jumu'ah. Jurists have mentioned that being overcome by sleepiness and hardship are among the permissible excuses for absence. But this should not become a habit. Absence from Jumu'ah without a legitimate Shar'i excuse is a great sin, and severe warnings have been confirmed for those who fail to attend it. Its virtue in expiating sins has also been mentioned. So, be keen to attend it to the best of your ability.