This is not a simple question and so is the answer. You need to choose your starting campus that is either Singapore or Fontainebleau when you are applying to to INSEAD. Once admitted you will be informed about your home campus – the campus where you will spend your first four months called Period 1 and period 2. The four most intense and fun months that you will ever encounter.
Campus exchanges begins from period 3 and there are several possible combinations that you could do. Abu Dabhi, Singapore (vice versa if you started in fonty), Wharton and Kellog exchanges. There is no compulsion to change campuses. There are some who just stay in single campus for the whole term. We lovingly call them lifers.
The normal pattern is to stay in the region where you want to get hired during the recruitment season. Period 4 is the main recruitment season, so make sure you are present in that campus during P4 based on your target geographies. Some common trends are as follows:
If you are a J batch that is graduating in July then the main graduation ceremony (P5) happens in Fontainebleau and if you are a D batch that is graduating in December then the main ceremony is in Singapore (you can guess that this is because of weather). Accordingly P5 most of them will be in Fonty for J batch and vice versa for the D batch.
A typical J batch scenario starting in Fonty would look like this you will spend P1 and P2 in Fonty. Do an exchange in P3 mostly to Singapore and in some cases to Abu Dabhi and come back to Fonty for P4 & P5 (as graduation also happens in Fonty for J batch) if you are searching for jobs in Europe or stay in Singapore for P4 only and be back in Fonty for P5 (this is usually tricky as the fonty campus will be full by that time and same is true for singapore for the D batch) and finally you could do P3 to P5 bundle in Singapore.
Alternatively you could start in Singapore and stay P1 to P3 there and do P4 & P5 in Fonty. You can make any combination that suits you but remember there are limited seats so its not necessary that you might get what you want. This is entire process is orchestrated through a points based bidding system. In short every one will get 200 points and you use them to bid for both electives and campus exchanges.
If you choose to be in one location for the next three periods (i.e after p1 & P2) then its called a bundle. Bundles are easy to get as you should commit upfront to stay in a campus for the next two periods.
So you have to be in the campus / region where you want to find the employment this is the standard rule. If you have prior European experience and want to find a career in Europe you should aim to be in Fonty for P4 and vice versa. An important point to remember here is that for Consulting roles in Europe it does not matter much whether you are based in Europe campus or not. On the other hand for Consulting roles or for that matter for any Asia roles its crucial to be based in in Singapore campus.
To conclude INSEAD is one of the few schools in the world (or may be the only one) that gives you so many options to choose for your geographic preferences. I only gave examples of Singapore and Fonty in the post but there are some who did Singapore, Abu dabhi and Wharton exchange. So like all things MBA related know what you want upfront and plan accordingly.