Artisans charging the reduced rate of 5.5% TVA?

At the present time this is not an issue as I have not reached the TVA threshold yet. In preparation though please can you clarify the following for me. I have a French registered company classified as Revetements des Sols et des Murs. At the present time I install mainly and supply very little materials to my clients. Sometimes I fit / install direct for the client / home owner and sometimes I fit for retailers in their clients properties.

It is my understanding that once I reach the TVA threshold when working on domestic properties, which are over 2 years old, where I am replacing say a floor covering - a reduced rate of TVA at 5.5% should be charged on my labour costs providing my customer is the end user, i.e. the home owner. Further to this I understand that if I supply and fit the replacement flooring on domestic properties, which are over 2 years old, the TVA on materials used should also be charged at the reduced rate of 5.5% providing the customer is the end user, i.e. the home owner.

It is also my understanding that if I fit for a 3rd party / retailer and not the home owner I should invoice the 3rd party / retailer at the full 19.6% TVA as they are not the end user and do not benefit from the reduced rate of TVA scheme. I heard that this because the 5.5% reduced rate of TVA is primarily given on the labour and when materials are provided as part of the overall invoice they attract the same reduced rate of TVA but goods alone do not.

To be clear in respect of all of the above, it is my understanding that a French registered retailer with no artisan status could not therefore legally engage my services to fit / install a floor covering supplied by his business and then charge his customer at 5.5% TVA on the supply of his services and the labour of my services. Would this be correct?