First off, what is it?

Supplementary (Duct) firing may be used in combined cycles in the HRSG – raising the exhaust temperatures from about 1112F (600 °C) at GT exhaust to about 1472F (800°C) or even 1832F (1000 °C).
http://www.stellar-energy.net/blog/2016/03/28/supplementary-...

Duct firing in the heat recovery steam generator (HRSG) of a gas turbine combined cycle power plant is a commonly used method to increase output on hot summer days when gas turbine airflow and power output lapse significantly. The aim is to generate maximum possible power output when it is most needed (and, thus, more profitable) at the expense of power plant heat rate.
https://asmedigitalcollection.asme.org/GT/proceedings-abstra...

For supplemental firing, duct burners are most often installed within the heat recovery steam generator (HRSG) inlet duct or between the HRSG final and primary superheater/reheater sections (more common in larger GTCC plants)
https://www.forneycorp.com/articles/duct-burner-without-augm...

"Some HRSGs include supplemental, or duct firing. These additional burners provide additional energy to the HRSG, which produces more steam and hence increases the output of the steam turbine. Generally, duct firing provides electrical output at lower capital cost. It is therefore often utilized for peaking operations."
https://en.wikipedia.org/wiki/Heat_recovery_steam_generator

From which we have learnt that 'duct firing' is also known as 'supplementary firing' or 'supplemental firing'. Which gives us a clue to finding the/a French for the term.

Et voilà !

"Combustion supplémentaire des gaz d’échappement La méthode de combustion supplémentaire à l'amont du HRSG est utilisée pour augmenter la température de gaz d'échappement à l'entrée du HRSG."
http://dspace.univ-tlemcen.dz/bitstream/112/15137/1/Ms.Gm.Zo...
(These Algerian theses are often very useful indeed)

Aux fins des présentes conclusions sur les MTD, une CCGT désigne les configurations avec ou sans combustion supplémentaire dans le HRSG
https://eur-lex.europa.eu/legal-content/FR/TXT/HTML/?uri=CEL...

For the purpose of these BAT conclusions, a CCGT includes configurations both with and without supplementary firing of the HRSG
https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CEL...

"le Secteur a indique 'que, du fait des grands brOleurs utilises places sur Jes parois el utilises pour !o combustion supplementaire du HRSG, las emissions de NOx de 10 turbine 6 gal pourroienl augmenter de 10 - 20 mg/Nm3. Cetle augmentalion e,' due aux temperatures locales elevees de ces brOleu(s Cl conduction. Par consequent. le niveou associe aux MTD dons le cas d'une combustion supplementalre devroii etre de 60 - 140 mg/Nm3 ."
https://inis.iaea.org/collection/NCLCollectionStore/_Public/...