Les Cracks (1968), a French comedy film about a bicycle race
The film you're looking for appears to be Les Cracks (1968), also known as The Hotshots in English. It's a French comedy that revolves around a bicycle race.
The movie tells the story of an inventor who creates an innovative bicycle and enters a racing competition. Throughout the race, he and the other competitors encounter various obstacles and comedic situations.
One scene in particular aligns with your memory: the racers come across a closed railroad crossing gate. Instead of waiting for it to open or finding an alternate route, they simply lift their bicycles over the barrier and continue the race. This closely resembles the wall-climbing scene you described. This gate-climbing scenario occurs again later in the film.
In another scene that aligns with your recollection, the protagonist's bike experiences brake problems, causing him to veer off-track and careen downhill. He crashes through a couple's picnic, disrupting their meal and slicing through plates and food with his bicycle wheels.