English term (edited): 3/8” hose barb

That's what a 'hose barb' is, anyway

I'd suggest keeping the 3/8", as it is a standard size, not merely a dimension, and even here in France, many plumbing fittings for example continue to use standard exact Imperial sizes. You might want to put the metric nearest-equivalent conversion in brackets, though, just to give people an idea — though it might be best to say 'env.', since although 3/8" and 10 mm would be close enough for the hose side, of course the threaded side of any such connector would be incompatible.

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Note added at 1 heure (2014-06-17 07:17:49 GMT)
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Please note that on these Imperial pipe / union sizes, the nominal dimension given always refers to the inside diameter (= bore) of the fitting, and not to the outside diameter (which is what corresponds to the actual hose size, given as ID).