International flight missed because of delay in national flight - Compensation options?

We wanted to take the following two flights on the same day.

Had the national flight been on time, we would have arrived at the airport 3 hours and 15 minutes early.

However, we missed the international flight by quite some margin. We were at no point offered any compensation, meal vouchers, hotel vouchers, refunds etc., even though we explicitly asked for it.

Is there anything we can do? The incident occured about one month ago.

National flight (ticket purchased days ago, one-way)

• In Peru
• CUZ to LIM
• Airline: Peruvian
• Gate closed according to ticket: 12:40
• Departure according to ticket: 13:10
• Arrival according to ticket: 14:35

2-leg international flight (ticket purchased months ago, return flight)

• From Peru to Germany (EU)
• LIM to MUC via CDG
• Airline: Air France
• Gate closed according to ticket: 17:50
• Departure according to ticket: 18:10

Summary of how the day went

• 11:10: We arrive at the airport and receive a boarding pass which states
  • Flight P90218, Gate 3
  • Gate closes: 11:35 (??)
  • Boarding time: 14:45 (????). Since this is still well within our time plan, we don't press the issue (stupid decision on our part)
• 14:35: Gate 3 is occupied by a different airline (who won't let us board, ofc). We search all of the other gates and find not a single employee of Peruvian. We leave the security area to ask for help at the Peruvian check-in counter. We tell them about our connecting flight. They ensure us that all will be fine and tell us to go back and "wait between gates 3 and 4" (seriously.)
• 15:21: The flight appears on the departure displays. Gate 5, boarding time 15:45. There is no speaker announcement, so we only saw this by pure luck (Gate 5 is on a different floor in CUZ airport and there is no departure display "between gates 3 and 4").
• 16:03: Boarding actually starts.
• 16:37: Airplane departs gate.
• 18:31: We arrive at LIM airport, 3 hours and 56 minutes late. We immediately hurry to the Air France check-in counter, but of course they confirm that we have missed the flight. They tell us to call the Air France hotline because they can't help with booking a replacement flight themselves.
• 18:44: We ask for help at the Peruvian counter. One employee helps us with calling the Air France hotline. However, Air France demands that we show up at the Air France counter in order to prove that we are late instead of no-show. The Air France counter is closed. The Peruvian employee calls the Air France hotline themselves, and manages to convince them that we are at the airport. After an hour on the phone (!) she tells us that Air France will book us on the same flight next day for an additional payment of 530 Euros per person and will send us an email with the details next day in the morning. We do receive an apology (the first of the day).

Next day

• We never receive the promised email
• We call the Air France hotline; they tell us that we should talk to Peruvian because Peruvian is responsible for providing a replacement flight. We tell them that we already tried. After countless hours on the phone we manage to get an agreement with Air France, for 480 Euros per person.
• We go to the Peruvian counter and ask for written confirmation of the delay. We receive a Constancy letter which states that we were on the flight P9218 which was DLY due to weather (this is the first time we hear of a reason, but the reason is entirely unbelievable to me). We ask for written confirmation of the arrival time, but they refuse.
• We go to the Air France counter and ask for written confirmation that we missed our flight because of this delay, but they only put their stamp on the constancy letter, without any additional comment.