The KLM/AF websites only allow(ed?) to choose between the cheapest, and a flexible fare. They do/did not allow to choose any fare that is published.

In some cases one may want to book, for example, a non-flexible fare in a higher fare bucket. Or a flexible fare, however not the cheapest one, in order to be allowed to upgrade to business class for a low(er) amount.

To book a specific fare I would indeed use ITA matrix to get an idea of what is available, the prices, and the fare rules. Then call them up and request to be booked into that specific fare class. Do keep in mind that there may be a service charge when you book over the phone.