You are a free human being and therefore you always have the freedom of applying. The question is only whether the application has any chance of success.
In general, if you have been refused a visa in any country anywhere, you want to display a change in circumstances on your next application. This is outlined by many answers all across this site. Reapplying under the same circumstances (same trip planned, no change to one’s situation, employment, finances, …) is typically doomed to result in another rejected application. However, the change of circumstances must also make sense; you cannot, for example, acquire a lump sum of money, put that on your account and call it a change in circumstances.
In your case, your train of thoughts seems to be ‘I was rejected by France so maybe I should try Finland for the same trip; I need to visit both countries equally long.’ In one word: don’t! This will be exactly the same application except that the country you are applying to is different. Schengen countries share a lot of information about travellers and issued/rejected visas in databases among themselves. Finland will perform a database check and they will find your previously rejected application with France. This will result in:
- extra scrutiny because you are applying again after a very short time
- extra extra scrutiny because you have simply swapped your main destination; this reads like visa shopping (choosing the country with the largest hope of success).
After those two layers of scrutiny, I would be extremely surprised if the Finnish officer comes to any conclusion other than reject.
The rules at which Schengen country you should apply for a visa are very clear: the main destination by days spent; if that leaves ambiguity the entry country. Applying for a visa with any other country will immediately raise suspicion that the person has applied in hope of the highest success rate; this will immediately reduce the applicant’s credibility. Reduced credibility means reduced chances of success.
Finally note that they concluded you cannot be trusted to leave Schengen at the end of your visa duration. That rings like very serious news; the assume you want to go undercover. Without being a lawyer, I would strongly suggest you do not try again unless you have gotten good legal counsel by one or until your circumstances — especially the ties to your home country — have changed significantly.
(This last paragraph is an extrapolation of many answers I read concerning UK visas. If Schengen visas are notably different in this respect, I would welcome correction in the comments.