Note that the UK company is fully owned by a french company.
A UK company would inherently be UK resident
Do you mean branch?
Or do you have no UK resident directors and don't want to travel to the UK? In which case you may need to work with a French bank's foreign currency account.
Should the question be this?
"I am a French company. I have employees in the UK. How do I go about paying their salaries?"
If that really is the question, I'm sure there are people here who can arrange all of the salary administration, including taxes, etc. As long as you pay them in advance, you do not need a UK bank account.
If you decide to open a UK bank account you can use BACS to make bulk payments and pay all your staff from a file exported from your accounting software.
The BACS Direct Credit service is described here:https://www.bacs.co.uk/Services/bacsschemes/bacsdirectcredit/Pages/BacsD...
Alternatively you can use a BACS approved Bureau to make the payments from your UK account to your employees on your behalf.
Details of BACS Bureaux are available here:https://www.bacs.co.uk/Services/Bacsapprovedservices/Pages/ApprovedBurea...
Not so easy!
UK banks are hesitant to open accounts for non resident companies.
Unless the company is tax resident in a country with a suitable DTA with the UK, it will be UK tax resident