TL;DR: As of today, no study found showing the effectiveness of Tegarome for any treatment. As of 12th Feb, I sent a message to the laboratory asking for a link to said study.
Looking up the product, I found one with the following statement:
In addition to that, the results obtained with this preparation have never been denied and have been the subject of scientific studies*.
- Recent studies, carried out in vitro by the galenic laboratory of the University of Besançon, confirm that Tégarome has anti-inflammatory, antifungal and healing properties, and respects the cutaneous bacterial flora useful.
No link to said study was provided.
Searching on the university's website wielded no results, except that they were offering formations in aromatherapy and phytotherapy. I did find the name of the laboratory who made the product:
Laboratoire d'aromathérapie Cosbionat - Fabricant exclusif des produits
aux huiles essentielles du Docteur Valnet
The lab's website is available here, also in french, with the same mention that a study has been done, but with no link available.
I only found a very brief analysis (original link in french) indicating a case of dermatitis apparently caused by Tegarome, which was reported to trigger an allergic reaction, but no mention that it was used to treat burn or such.
The lack of evidence thus far indicates that the effectiveness of Tegarome for treatment of burns and skin injuries is unknown.
A message has been sent to the lab responsible for producing Tegarome as of 12th Feb 2020, awaiting for a reply.