How were germanic groups able to cross into gaul in
a. d. 406?

The vandal, sueves and alans which is the Germanic groups crossed the river rhine which is the boundary of the empire when it was frozen. The roman had deteriorated this border because they need to redistribute their troops in this area to italy to fend off an attack of italy by an ostrogoth king. The roman empire already had much trouble possessions its extremely long borders sufficiently patrolled. These were the times that roman emperors trailed each other in quick succession and most of them were generals of border legions that were proclaimed emperor after the fall of the previous one. The aspiring emperor then took most of his troops elsewhere to make good his claim. Likewise, at the time most of the Roman border troops in gaul consisted of non-romans, many of them from germanic tribes. They drive hindmost germanic immigrants if underneath strict commands to do so but would look the other way understaffed as most crowds already were if gone to their own strategies.