First of all, there is no interest on depositing euros, and there is a charge for withdrawing cash abroad. It is equivalent to using your own money and giving it to the bank.

Suggest this: call the credit card customer service to increase the temporary limit, which will generally work. And carry cash with you, not all parts of Europe can use credit cards.

As for the second method you mentioned, it is also feasible. You can apply for online banking and use online banking to deposit money on your card. Of course, it is also feasible to let others help you repay the money at the counter.

I don't know how long you will be gone. Generally, an official tourist visa lasts for at most three months, and it is enough to use a credit card (salary) of 2,000 euros per month, but it is best to use cash1000-2,000 euros per month, because there are many things that need cash, such as tips (which are not needed in France, and tips are included in meals).