Removing space between objects of a shapefile
Yes, you can physically move the polygons of the outer territories in geographic data, but this would degrade data unnecessarily.
The much better solution hinted at by @ThingumaBob is to simply use multiple map frames when designing your export. Create a map frame for each outlying territory, then move those around on your sheet layout for printing/viewing the result version. This also allows you to use different scales for each departement, add labels and much more, if desired.
Check the QGIS documentation on how to accomplish this.
As a basic rule: Most GIS will separate data exploration and analysis from actually rendering and exporting map products, because there are many very valid reasons to depart from geographic 'truth' for the sake of readability of a map product.
d3 the correct way to do this is to use a composite projection. Here are plug-ins that specify composite projections for France:
- https://github.com/rveciana/d3-composite-projections (d3v4 and d3v3)
- https://github.com/seeschloss/francedom (unmaintained as of 20.12.2019)