Since you can't get another appointment, your best course of action is to apply to the French consulate and hope. If they decide that they are not competent to accept your application because of your itinerary, they will refund the application fee.
Your chances seem good, however. Because you will in fact be spending more time in France than in Germany, they are likely to accept the application. Your transit in Germany doesn't likely count, so you'll be in France for a day longer than in Germany (that is, you're spending four nights in France and only three nights in Germany).
Note that the itinerary you describe constitutes a ten-day trip, because you arrive on Saturday and leave on Monday, and because presence in the Schengen area is always counted on the basis of calendar days or any part thereof. This is important because we've had at least one question where someone submitted a visa application with miscounted days, and the consulate granted the visa without correcting the error and without adding any padding, so the granted duration of stay was actually insufficient for the trip he was planning.
The rule about your port of entry only comes into play if you cannot determine a main destination for your trip. If the French consulate decides that you have no main destination, they may decide to reject the application and direct you to apply at the German consulate.
The assertion that France is your main destination would have more weight if there were some specific reason that you were going to France, such as a conference, a concert, an exhibition, or another event. Of course, that case would be correspondingly weakened if there were other such events in the other countries you're visiting.