The measures targeting British fish exports would include "systematic customs and sanitary checks on products brought to France and a ban on landing seafood", French government spokesman Gabriel Attal told reporters.
Europe Minister Clement Beaune said extra checks could also be extended to "other merchandise" by "reinforcing our procedures and controls compared with current practices".
The latest spat between the neighbours was sparked by licensing rules for EU fishing boats wanting to operate in waters around Britain and the Channel Islands after Brexit.
France has been incensed by the rejection of French boats by Britain and the self-governing Channels Islands of Jersey and Guernsey, which depend on London for defence and foreign affairs.
While targeted measures for the fishing sector would hurt British exports, broader customs checks have the potential to seriously slow down trade with the UK.
British fishermen, who export most of their produce to the EU, are highly dependent on French ports as a gateway to the Continent.
France "will not let Britain wipe its shoes on the Brexit deal," Attal added.
The flare-up over fishing is the latest in a series of disagreements that have plunged diplomatic relations to their lowest point in decades.
As well as tensions over migration, Paris was outraged in September after Britain helped broker a deal to supply Australia with US nuclear submarine technology, leading Canberra to scrap a mega-deal with France for conventional submarines.
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