Fullcalendar - Can we add custom data to our event Json Data?

Try It with events: instead of eventSources:

$('#calendar').fullCalendar({

 events: [ 

{"id":"46_l","title":"CustomEvent-Chargement","start":"2013-12-02","end":"2013-12-03","className":"customEventsClass","type":1},
{"id":"46_d","title":"Custom Event-Livraison","start":"2013-12-11","end":"2013-12-12","className":"customEventsClass","type":2}

]

});

As per the documentation:

Non-standard Fields

In addition to the fields above, you may also include your own non-standard fields in each Event Object. FullCalendar will not modify or delete these fields. For example, developers often include a description field for use in callbacks such as eventRender.

Example:

$('#calendar').fullCalendar({
    events: [
        {
            title: 'My Event',
            start: '2010-01-01',
            type: 1 // Custom field
        }
    ],
    eventRender: function(event, element) {
        console.log(event.type); // Writes "1"
    }
});