Can I get a green card when traveling to Australia with a French passport?

No. According to the relevant regulations on obtaining a green card in Australia, the following conditions need to be met to obtain a green card in Australia:

1. The applicant's occupation is on the occupation list required for the Australian 189 visa.

2. Pass the career assessment.

3. The EOI score is no less than 65, and the applicant has been invited by EOI.

4. The applicant must be no more than 45 years old before the date of receiving the immigration invitation.

5. Applicants must have at least 4 IELTS scores of 6, or equivalent TOEFL, PTE or Cambridge English test scores.

6. Good health and no criminal record.