"The benefits to French GDP are not mainly from the tickets, but from the tourism-related revenue (hotel stays, restaurants, flights, &c)." yes, you can infer that from the last sentence in my previous comment, but still, they do not monetize it as much as they can because they could have decided not to make the entrance free for the youngsters and they would make more money even if the number of young visitors decreases.

The difference with the google search engine is if you are not willing to pay and so do not use the search engine then google won't make money at all from you whereas few people will decide no to go to Paris just because the Louvre entrance is not free.