It is impossible for a Spanish Civil Guard car to cross the border with France with lights and siren on just to drop off passengers at Perpignan station. In special cases, such as combating terrorism, the police of one country can cross the border, but they must always notify the authorities of the other country beforehand. Clearly, this is not the case in the film, and no Civil Guard officer in their right mind would do such a thing.
The police officers who intend to recover the stolen manuscript say they must do so before the thief crosses the border into France. This implies that once the thief leaves Spain and enters France, they will no longer be able to do anything. In reality, this is not the case. The Spanish police can perfectly coordinate with the French police to arrest the thief. The arrest of the thief is a previously planned operation, so they have plenty of time to alert the French police. Moreover, Spain and France have agreements that allow the police of one country to cross the border into the other in exceptional cases, such as combating terrorism. Furthermore, the Spanish officers on the train have no choice but to cross the border with the thief because it is the train that crosses the border.
Access to the high-speed train platforms in Spain is through a control similar to (but not as strict as) that of airport terminals. It is impossible for someone who is not a passenger to access the platform to say goodbye to or welcome a passenger, as seen on several occasions in this film.
All high-speed trains that stop in Barcelona do so at Sants station on underground platforms. Sants station is in the middle of the city. The Barcelona station seen in the film has an outdoor platform and no buildings around it, clearly indicating that it is a suburban station located on the outskirts.