She will need a visa to come to the UK to marry, or if they marry in France she will need a visa to join her husband. (The Children won't need visas, as they are French Citizens although watch out for post-Brexit changes)
https://www.gov.uk/join-family-in-uk
Five-year route: The process will be a 2.5-year visa, then another 2.5-year extension and after five years in the UK fulfilling the requirements such as the minimum income requirements, English language skills she can obtain ILR.
Minimum income required is - £18,600 per year
There is a different option for her as well;
Derivative Rights of residence (Does not lead to ILR or PR) as a parent of a child with the right to live in the UK.
I don't know much about this and with Brexit might be a risky route to take if it is scraped in the future following the UK's withdrawal from the EU but she could claim derivative rights to live in the UK as a Parent of a child/children who have the right to live in the UK however this does not lead to ILR or permanent residency under the EU laws maybe she could qualify for the ten-year long residence route?
https://www.gov.uk/derivative-right-res ... ligibility
