HK Post wants about H$350 to get a 3kg parcel from HK to France. That works out to about $45.
$370 did sound particularly egregious, but I just checked UPS' online quote site[1] and got a quote of $311-394 for a 5 pound, A1 sized package from California to Paris.
I'm not quite sure what A1 sized is (ISO A1 paper? Amazon A1?) but at 5 lbs USPS quotes between $60 and $130 to go from San Francisco to Paris. For international shipping from the US, the private companies will almost always be significantly more expensive and potentially leave you on the hook for expensive customs brokerage fees.
OTOH if you want to ship it express (Global Express Guaranteed — GXG in USPS speak) that comes out to around $265 (less if you pay online) and not all post offices will take GXG packages. $60 to $265 is the difference between a 1-3 business day expected delivery time and 6-10 business days.
$370 did sound particularly egregious, but I just checked UPS' online quote site[1] and got a quote of $311-394 for a 5 pound, A1 sized package from California to Paris.
In my experience in Asia, Fedex, UPS, DHL etc. provide substantial discounts to customers with accounts, but one-off quotes to the US/Europe are typically very expensive.
[1] https://www.ups.com/mobile/quoteService