I have the impression that the GP practises in Belgium are similarly organised to France. To accommodate to the personal needs during the last few years, it has become much more common to have practises with several GP’s working together. In that way the would in the first place be able to cover for one another, have better personal working hours/periods, etc …
Additionally, as we tend to know more together, that also would be an advantage. Within that proctise, they are still self-employed bit also with some additional security built in.
Within the practise as a patient you normally go to the same doctor every time. That would be more personalised care, they do get to know you, etc …
As far as hospitals are concerned, there is much more support in terms of nurses, administration, etc for the specialists working there. To be able to easily have an appointment there, a specialist assistance need should best be requested by a GP.
Hospital insurance, etc … is mostly done electronically by means of a card or similar (number, …)