Well Germany could promise parts of the French empire in Africa.
Theis could prevent Britain from joint WWI in 1914 what are the effects?
French Flanders could also be offered to the Belgians, but I'm not sure how much the Belgium would actually want more territory in Europe.
What would be ideal of course if for the Belgians to let German trains pass through. Even on short notice the Germans could move a good sized body of troops to a jumping off point in the west of Belgium and keep up supploies far more effectively than OTL. But even without this the German attack on France would be considerably more efficient. Troops would be able to make 'administrative' marches, in transit rather than battle order and train lines would be available to bring up supplies without enemy action or sabotage. This would get them into northern France faster and fresher than OTL, and with the armies in closer contact with each other.
This would give the Germans that bit extra oomph they needed to hold on the Marne and probably win the Race to the Sea. It wouldn't make the Schlieffen plan succees (nothing short of massive investment in trucks and a rethink of the whole operation would), but it would place Germany in a better position for the grinding attrition ahead.
Is there then a chance the French will pre-emptively invade Belgium? (or do it as soon as the Germans enter Belgian territory.)
They wanted to IOTL. The British were very much against the idea, though, so they planned to head in further south.
I'm not so sure that the British were as much against the idea before the war as they have made themselves appear to have been after. If push had come to shove on the issue, I think the British would have pressured the Belgians to let the French in.
However, in the mass mobilizations thru out Europe the Belgians did originally mobilize with the bulk of their armed forces along the French frontier. They had long suspicions about French advances and were pretty stunned when the ultimatum arrived from the Germans.
If prewar plans existed for Belgium to allow the German army to mobilise and assemble in Belgium then of course the French would react. But if in response to German demands during mobilisation the Belgians capitulated and allowed the Germans to transit it wouldn't be too hard for the Germans to run some of their later troop trains and supply trains into Belgium itself. Certainly much easier than for the French to completely change the direction of their mobilisation to counter it.
Imagine the benefits if the Von Kluck's army got to the Marne a couple of days earlier, having marched 50 miles less, having suffered less battle/marching casulaties and being less strung out?
As for a POD, the Belgians just being scared of Germany, and knowing that they will march through anyway may be reason enough to allow the transit.