For sleeping outdoors, yeah, you would need a sleeping bag system that is both lightweight and provides enough insulation to keep you warm on very cold nights. The military does make such systems, but for walking the Camino and staying in albergues, it's not necessary.
Marmot and REI both make good bags rated around 40-55C that are lightweight, pack small and and reasonably priced. If you want to add some versatility to that system, bring a lightweight liner, too.
That should cover all your bases.
I don't have a brand to recommend -- the French Army one I had was a defunct model I've never been able to replace.
(I've got something similar, but it's heavier than what most would prefer, but then I sleep outdoors more than most too)
For colder weather with a risk of sleeping outdoors or in cold
refugios I'd anyway recommend a sports sleeping bag for most people, not military. Sports ones are better than military in those conditions for
hikers on the Camino, because the cold-weather military equivalent is simply too heavy.
The great thing about the ultra-light military ones though, in normal Spring to Autumn conditions is that they're specifically designed to be easy to pack and lightweight, and you get combined use from them as a bed cover, blanket, an airy sleeping bag for warmer nights unzipped, and a snug sleeping bag for cooler ones zipped tight, because they are also specifically designed for unpredictable, variable ground conditions.
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But yeah, for a Summer Camino on the
Francès the only real problem with finding a bed unless you're very impoverished is the risk of crowds so large that no beds are available -- which has been happening occasionally since the last Santiago Holy Year. So some sort of bag can be advisable, but for most non-impoverished people the absolute ultra-lightest one you can find. But if you avoid certain very specific periods -- ie just before the Feast Day, or bang in mid-August, or bang during "the crowd-avoiding September crowd"
, yes it's perfectly feasible to go without a sleeping bag entirely -- although not having one does actually curtail your freedom on the Camino to some degree.
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But given the OP's project of an off season March Camino on a secondary Way, I'd definitely recommend a sleeping bag as being
necessary, not superfluous.