While I don't know what visa checking system Ferry's use, I know that airlines use TIMATIC
The result show only "Family Member Residence Cards issued by United Kingdom to family members of an EEA nationals" is accepted by France.
UK ILR is not mentioned as being exempt for Schengen Visa
From this, it means you need to apply for a Schengen Visa.
Worth to point out, other Schengen Countries, e.g. Poland accept UK ILR
Checking airlines database
https://www.klm.com/travel/sg_en/prepar ... saform.htm
National Philippines (PH) /Residence United Kingdom (GB)
Embarkation United Kingdom (GB) /Destination France (FR)
France (FR)
Passport required.
- Passports and other documents accepted for entry must be
valid for a minimum of 3 months beyond the period of
intended stay.
Visa required, except for A max. stay of 90 days(SEE NOTE
53781):
NOTE 53781: The max. stay is granted within 180 days.
- for holders of "Family Member" Residence Cards issued by
United Kingdom to family members of an EEA national