The plan is seen as a test of President Emmanuel Macron's determination to pursue a far broader raft of economic and social reforms during a term that runs to 2022.
"I was introduced to President Macron by Tajani ... as the "enfant terrible" of the European Parliament and Macron smiled and said 'I know, '" Farage said in a statement tweeted by his communications officer.
"I want to be part of a generation that will defend European sovereignty, as it is the only way future generations will be able to decide their future".
Addressing the EP in Strasbourg, Macron said his speech came at a time of "division and doubt" within "a number of European countries".
Macron admitted Tuesday that air strikes in Syria "solve nothing" but said France, Britain and the United States had been forced to step up and defend the "honour" of the global community. "These strikes don't necessarily resolve anything but I think they were important", he said.
Macron is planning to meet with Merkel on Thursday.
He said Tuesday France is ready to increase its own contribution to the EU budget and insisted European countries should work on more closely harmonizing fiscal systems and tax levels.
Reported overnight missile strikes in Syria false alarm
The move is likely a warning from Syria that it has the capacity to hit back at the West if it wants to. Syria's Sana Ajel news claimed anti-aircraft units responded to an attack in Shayrat airbase near Homs.
European Parliament President Antonio Tajani also attended the lunch meeting and, according to Farage, introduced him to Macron as Parliament's "enfant awful".
He said: "I will only support an enlargement when there is first a deepening and a reform of our Europe".
Macron will meet with German Chancellor Angela Merkel in Berlin tomorrow, as France and Germany aim to agree on proposals for European Union reforms by June.
European Union leaders are set to adopt preliminary Macron-backed plans for eurozone reforms and for an overhaul of its troubled asylum system in June, but there is still a lot of work to do.
He is also expected to push for deep reforms of the 19-nation eurozone.
She made a joint speech with then-French president Francois Hollande in Strasbourg in 2015 in which they urged unity in the face of the migrant crisis.