A lot of Frenchmen were already miserable enough and have nothing to lose but their lives.
In regards to safety,the same can be said about the colonies of other countries in the Americans.The 13 colonies and the Portuguese ones weren't safe to begin with either and were fairly miserable when they first started.
As for Louis XIV's move to the Versailles,it was partly due to a fear of the urban poor.During the Fronde,the mob stormed the palace and even entered his room.They only left him alone when they found that he was asleep.Dude was absolutely terrified of the mob and don't want to experience that anymore.
The urban poor was always a security threat--as indicated when they stormed the Tuileries during the Fronde.When I'm talking about urban poor,yes I'm talking about vagrants,people who are out of work.
Naturally,some funding would have to be put in place to send these people overseas.
As for your notion of British colonies having people pay to get themselves to their colonies--that didn't happen in the penal colonies.
What is your source on this ?
I never heard anything like this, so I searched a bit, and the only thing I found is a footnote saying that during a day of January 1651, the mob entered the Royal palace to see the King.
It is not given an importance as big as the one you confer to that event, so I'm having trouble to picture the construction of the greatest and most expensive palace of its time decided on a single minor event.
Back to the OP, we need to determine what part of New France we're talking about, as Québec is very different from Louisiane; as well as when.
OTL there was an attempt of sending more settlers to Louisiane under the Regency (ie. urban poors, prostitutes, the fringe of the society), but it was still on a small scale.
In my opinion, using force was not the most effective way to attract settlers there. [There was an hilarious scene about this in "Let joy reign supreme" of Bertrand Tavernier, where they round up the delinquents, marry them expeditiously before sending them in Louisiane.]
Plus, a big chunk of these people will die during the trip, and the rest within the few first weeks after settling due to various diseases.
To make a real difference in the population, I think the only way is the one went by Viriato on his (great) TL : An earlier settlement of New France.