Social Security is a called an "insurance program" although it is completely unrelated to conventional insurance. The closest financial instrument is a Ponzi scheme, which is illegal under US law.
Health coverage goes to some entity that isn't the government and is usually optional, so it's viewed as a benefit and taken into account when computing total compensation.
Unemployment insurance on the other hand is taken out of every paycheck and handed to the government without an opt-out. Yes, of course you get something for it; the whole point of taxes is that society gets something in return. They're still taxes.
With respect to claims of wanting to underpay employees, I don't think that's something anyone is actually arguing for when they talk about unfriendliness toward startups. The French government is levying a high _proportional_ tax to cover _fixed_ fees like health care. This can make sense at a societal level as a form of wealth redistribution, but it's a disadvantage for high earners like those in the software industry. Those employees can earn more in other countries with the same cost to their employers simply because less is taken out of their paycheck, and because the difference is more than enough to cover fixed fees like health care it's a good move for them to do so. The people being disadvantaged aren't startup employees (not passing a moral judgement -- the claim itself just seemed off).
In English it's all translated to "tax" and rightfully so. English languages and cultures don't have subtle semantics like French does. For example everything in the UK is a tax, corporation tax, income tax, council tax, etc... (one exception being the UK national insurance).