Except both nations need to agree to deploy the integrated units.
If both were integrated into a continental military, which would be pleasing to German federalists and acceptable to the French, then command would be in the hands of a single European HQ which would decide upon deployments. Neither wholly German nor French, this HQ would not arouse indignance or anger, at least in theory, to the deployment of troops from either. It would also by consequence, herald the European Union not as nations, but as a continental state - an interesting development no doubt, whatever your opinion on such a thing.
Which, granted, you could argue that Germany could soft-power strong-arm them into agreeing. But in that case, what's different than now? Germany could just as easily strong-arm the nation into deploying its army whereever it wanted them to, so integrating them doesn't change much there.
So far, the low-profile and ad hoc approach of the Framework Nations Concept has worked to its advantage; few people in Europe have objected to the integration of Dutch or Romanian units into German divisions, partly because they may not have noticed. Whether there will be political repercussions should more nations sign up to the initiative is less clear.
The most obvious difference is in public reaction, this would be the sneakiness referenced earlier
Germany could strong-arm them and the resistance would be fierce - not just in the countries being bullied, but within Germany itself (German public is opposed to using German force against weaker nations). This method will in the long-term cause all of these smaller states to become militarily dependent upon Germany for their defence, once that is secured they will be politically dependent upon Germany. This will in turn cause friction wherever Germany's needs and agendas diverge from its dependencies. By contrast Germany constructing this force through the EU would entail the same concentration of military power, with a lesser risk of world powers or public opinion looking on in caution at German power consolidation - because Germany herself will be sacrificing much of her own sovereignty in order to push a continental military. For now, under such a framework, Germany will be the core of this structure while the smaller nations form its periphery, unable to act without the consent of Germany and unable to act against the will of Germany. This is the most significant difference between similar arrangements already existing now between France, the UK and their allies - neither of the former two are forming permanent military units subsuming the brigades of their allies into their military. For example, Britain leads the JEF under the Framework Nations Concept, the same one Germany is using. Under the JEF the UK trains with the Scandinavian and Baltic brigades, exchanging technical and operational resources and expertise, creating a framework from which a joint operational force could be deployed at a short moments notice. This is different in that there is no permanent military force - the UK is not transferring Scandinavian and Baltic armed forces into the British armed forces, in the manner that Germany is enlargening its armed forces.
Countries that form the cluster nations to the German core will over time become militarily dependent upon Germany, with their arms being supplied by Germany and their forces serving as specialized branches of the German army, their ability to act alone atrophying to nothing. Therein lies the issue, Germany can propose to send their soldiers to fight wherever Berlin wishes and they will have little recourse to reject Berlin, but the Germans will not allow their dependent partners to in turn propose sending German troops wherever these cluster nations wish. If Germany intends to form permanent military units with other countries, it should be as a European army, which would bypass this most critical problem.