Are there any issues if someone goes on holiday to France for 4 months in one continous period?
It takes more than a holiday to break UK residence
UK tax residence is not broken by someone going on vacation, regardless of how long this vacation is (extending even to years).
UK tax residence can only be broken by someone moving abroad permanently or indefinitely for a 'settled' purpose, for example to emigrate permanently or take up a foreign contract of employment.
The minimum period that can break UK tax residency is for someone to leave the UK for a foreign contract of employment for a minimum period of 1 complete tax year (6th April - 5th April the following year).
A 4-month holiday wouldn't qualify on any basis.
Do they claim tax credits?
There are different (statutory) residence rules for tax credits purposes that effectively mean that tax credits won't be paid after 8 weeks (generally this may extend to 12 weeks in certain cases) of absence from the UK.