would issuing new equity to overcome crisis affect the stock price?

In general, issuing and selling new shares shouldn't affect the price of the existing shares because the newly received money from shares is considered an additional asset.

But how about this case, rising capital to overcome a crisis?

Both are same. Additional shares bring in additional capital. The impact to current share price depends on various things, for example if the market believes additional capital can't be deployed or used positively, the price goes down... If the market believes that additional capital will allow the company to expand faster the price will go up.

In Air France what exactly will happen can't be predicted. But it would keep Air France afloat and operating, hence the price should be more stable.

Well, the long-term debt minus capital leases is $6.67B. Then the cash is $3.72B. But there is the possibility of a substantial loss of revenue for a year or more. It looks like the company needs $3B but the stockholder's market value is only $2.44B. Or the long-term debt including capital leases is $9.82B.

The country is planning on loans to the company. If those loans are written as senior loans than that gives the country a claim in a re-organization. Or the country could just figure on how much the company needs to make it's payments for one-year. The shareholders are saved for one-year but the airline's overall debt is increased.

The stock price would probably drop on a large issue of new stock but the company debt would be reduced. The stock price might hold on an issue of additional debt but then there are additional debt payments to make.