French term (edited): activite des societes holding

I would translate it like this

or business activities of the holding companies.

"Activities" here is the business.

But because the holding company conducts no business activities, it has almost no exposure to liability
http://www.toolkit.com/small_business_guide/sbg.aspx?nid=P12...

Business Activities
We adopted a group structure in which a holding company owns the shares in six operating companies in different parts of the property market.
http://www.grosvenor.com/About Grosvenor/Business Activities...

Magaret is right that you can use simply "activity" for a trade register. I often use the trade register online in the UK and here there are codes to designate types of business and they are called "activity codes", so I presume that activity would fit just fine here.

However, I did check for the trade register here and you can also use "business activity"

Principal Business Activities
This classification is based on the UK Standard Industrial Classification (SIC 03) Codes including sub-class revisions effective from 1 January 2003
http://www.companieshouse.gov.uk/about/gbhtml/gba2.shtml

… will do it for the whole line. Drop the parenthesis. And 'activity' alone is fine: the business of owning other businesses (and that's all it does) isn't much of a 'business' in the ordinary sense of the word.