If there was hard and detailed evidence that the Syagrian military were substantially Roman in discipline and tactics then this discussion would probably not be taking place. The trouble with history is that the theories grow but the evidence does not (or hardly does)
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I look at it this way: Procopius's account that the 'Arborychi began to fight for the Romans' some time in the 470's makes sense only as a recruiting drive by Syagrius among his own subjects, the Gallo-romans of Armorica, replacing his reliance on the Franks with a surer dependence on a home-grown army. It was this army that fought Clovis up to his baptism in 496/7 and persisted as units under the overlordship of the Franks after that.
Question is, what was the nature of this army's training, equipment and structure? There are two opposing theories, with plenty of gradations in between.
Theory A: the Roman military tradition in northern Gaul had been dead for decades by the 470s, i.e. there were no longer any disciplined units with experienced officers capable of training new recruits in the Roman manner. The only model Syagrius had when he recreated his army was the barbarian one. His troops were equipped and trained in the barbarian manner, abeit with Roman battle standards and in Gallo-roman clothing, and that is how they fought.
Theory B: the Roman military tradition did survive in northern Gaul. Old formations were intact, albeit reduced in size, and they formed the nucleus of Syagrius's new army which was trained and organised by them. This force, substantially Roman in character, kept its identity even after the fall of Syagrius, only gradually losing it in the course of the 6th century.
Well, you can take your pick, but let me offer a few arguments in favour of theory B.
Nothing proves that the Roman army entirely disappeared in Gaul in the mid 5th century. It is more likely that it was much reduced in size and no longer capable, by itself, of fighting large battles. Hence Aetius's need for barbarian allies to face the Huns. Procopius's affirmation that 'even at the present day they are clearly recognized as belonging to the legions to which they were assigned when they served in ancient times', implies that the old legionary formations persisted right to the end of the 5th century and beyond. The fact that the soldiers belonged to 'legions' seems to rule out the notion that they were barbarian foederati, as these kept their own tribal structures and did not organised themselves into legions.
Of course, one could cast doubt on Procopius's use of the word 'legion' just as one could cast doubt on his whole account, but I prefer to take it at face value unless there is solid evidence for not doing so.
The economic and social network in northern Gaul remained intact throughout this period, as, for example, the pottery record shows, hence the means existed to maintain the traditional Roman formations. If these were privatised by the landed gentry then their upkeep was assured.
One can question whether these formations preserved all the nuances of the old Imperial army, but what would have made for differences between them? The Roman Army had always been an autonomous entity - the troops owed loyalty to their generals, not to the Empire as a whole. This attitude would have remained intact even when there was no longer an emperor and the 'Empire' had shrunk to northern Gaul. What motivated Roman troops to keep their standards up would have remained in place even after 476. The one thing that would have degraded the Roman character of the army is if it had ceased to be professional: paid troops living apart from the general populace. Nothing suggests that this was the case in northern Gaul.
There's a parallel to this in modern-day Britain. With the British Empire gone the British army has remained as professional as it ever was - even more so. It just became smaller. If you don't have numbers but you do have money then the natural inclination seems to be to go for quality.
