Transition from PhD Astronomy to Quant

Hello everyone,

I will defend my PhD thesis in Astronomy - Celestial Mechanics, to be more precise, in December this year, but I still have a Postdoc contract next year if nothing changes.
My interest for Astronomy / academia wane as I go further in this direction and by now I would like to transition to a data science / quantitative finance jobs. My initial intention is actually data science but as I'm looking deeper, I found that a job as quant researcher is much more suitable for me.

I have strong background in computational physics / statistical analysis / stochastic process. Beside the required analytical thinking / problem solving skills for a PhD, I'm quite confident with my coding, which is primarily in Python, as my research for the last 4 years involves a lot of programing / data handling / parallel computing. I have great interest in machine learning and data science generally. I have implemented several algorithm of several papers that I found interesting in ML / statistics and I think I have no problems doing it for an trading algorithm in an analytical finance article for example.
Therefore I don't think I will have any problems transitioning to quantitative finance, I could be wrong though.

Now, I desire make the transition but I find the road ahead quite fuzzy and uncertain as I have no experience outside of academia before.
Should I apply for a quant job right now? Or I should spend a couple of months before to brush up my knowledge in finance, trading, and preparing for the interview?
More generally, what is the best path to take to make a smooth transition? Not only for me for future interested Astronomy graduates.

I'm an international student in France, by the way.