I just looked this up a few weeks ago.  French and English think about the soon to occur/certain to occur.  

English has something called the "Present Continuous".  

eg) I'm going to the store this afternoon.  (PC implies future action) 

eg) I'm going to the store right now. I'm almost there.  (PC implies present action)

Both use the same verb tense and there isn't a technical distinction between them. It's context dependent. 

In French there is no present continuous, but there are two ways of describing something similar.  The first is the phrase (not verb tense) "être en train de". Meaning it's happening right now and is a work around for the lack of a present continuous in French. 

The second is to use the futur proche - which implies something more close to now than the traditional futur.  

eg) Je vais aller au magasin demain. 

Thanks Evan, but I was thinking about the use of the English simple present and French le présent to describe the future, not the continuous present or le  futur proche (which is a true future tense, though it’s constructed like English continuous present). The example in the lesson is "His train arrives at ten tomorrow morning".

French has 3 ways to speak about Future events. Ranked according to their immediacy from happening very soon to happening at further into the future, they are:

1) Using present tense.
This works for events in the immediate future. To make it absolutely clear, there are often times added phrases like "plus tard", "cet après-midi", etc. One would translate this, as Evans mentioned" using present continuous form in English:

Je cherche Pierre de la gare dans une heure. -- I'm picking up Pierre from the train station in 1 hour.

2) Le future proche
This is exactly like the English "going to do something". It's for actions not in the too distant future.

Je vais faire les courses demain. -- I am going to do my shopping tomorrow.

3) Le future simple
Used for unspecified times in the future, usually farther into the future.

On verra. -- We'll see.