Can a rescue package be considered as a subsidy to the industry? In the BBC article, France announces €8bn rescue plan for car industry, it is mentioned that the car industry will be given a rescue package to avoid unemployment. Would this be considered as a subsidy given to the car industry?

If not, what is this microeconomics concept called?

Also, I read the statement:

"government would also give people upgrading to a less polluting car a €3,000 bonus, as part of a scheme open to 75% of French households".

I want to know what is this concept called in microeconomics;

the concept of giving money to the consumer for purchasing a good(the car), or rather an upfront discount by the government. 
I don't think this can be considered as part of the subsidy as well because it doesn't reduce the production cost. 

Link to article:

https://www.bbc.com/news/business-52814074?intlink_from_url=https://www.bbc.com/news/business/economy&amp;link_location=live-reporting-story
It can be considered subsidy, especially if you are asking for the quoted passage. Although looking at it directly the subsidy seems to de jure be on the consumption (this being said some or maybe even most of the benefit will be most likely captured by carmakers through the economic incidence of the subsidy). 

For example, following Mankiw and Taylor, economics 3ed subsidy is defined as:


  payment to buyers and sellers to supplement income or lower costs and which  thus encourages consumption or provides an advantage to the recipient


Under this definition the policy you explicitly mention above would definitely qualify as a subsidy.

In different textbooks wording will change but not in any drastic way (to the best of my knowledge).

However, a rescue package itself is not an economic term. It is possible that the plan also includes policies that could not be considered subsidies as well.