"It's a 50-minute flight but I can fly to New York more cheaply," he complains. Then again, eight airlines fly between Paris and New York. Only Air France and Lufthansa serve the Paris-Frankfurt route.
Which makes Mr Perelman wonder: what happened to all the talk about airline deregulation in Europe? No upstart airlines have swept in to spur competition on his route. He flies to Italy frequently too, but has yet to see big changes in fares there either. "Have I felt any benefits?" he asks. "Absolutely not!"
The European Union has been gradually deregulating the airline industry for 10 years, aiming to make air travel cheaper and more efficient, but the process only becomes complete on 1 April. As of then, any EU airline can offer domestic flights within any other EU country.
Unfortunately for passengers, there's nothing magic about this date. Even though regulatory barriers are coming down, it will take several more years before the face of European aviation truly changes, experts say.
And it will bear little resemblance to what happened in the US in 1978, when competitive barriers were dropped overnight, causing fares to plummet and scores of new carriers to appear - and then disappear.
"Liberalisation hasn't produced an American-type big bang in Europe," says Philip Lowe, the chief of staff to EU Transport Commissioner Neil Kinnock.
Aviation analysts agree. "The deregulation of the European market will be a less dramatic event than in the US," says Richard Hannah of UBS Ltd.
As in the US, deregulation is aimed at eroding the advantages enjoyed by established airlines in a traditionally state-controlled industry where regulators once ruled on everything from fares to the number of seats airlines could sell.
The biggest single step came in 1993, when the EU allowed airlines to fly to any other country in the union without the bilateral national treaties that formerly dictated service in the industry.
But big national carriers such as British Airways, Germany's Lufthansa and Air France still control the majority of landing slots at key airports, making it tough for the upstarts to muscle in.
The Association of European Airlines, the lobbying group for the Continent's 25 major carriers, argues that there isn't enough space in congested airports to accommodate annual travel that is expected to double in the next 12 years.
"On most routes you don't have the infrastructure - or the slots - at airports to allow three airlines to compete at 8am," says Karl-Heinz Neumeister, the group's secretary-general.
Start-up airlines such as Virgin Express, the low-fare carrier launched by Richard Branson's Virgin Group last year, ses it differently. Jonathan Ornstein, the airline's chief executive, says he would dearly love to get more slots at several airports - including Frankfurt, where Mr Perelman and his fellow travellers are paying the pounds 430 fares.
It can't get them, and Mr Ornstein contends that German authorities are protecting Lufthansa from rivals which could use slots opened after Delta Air Lines' decision in January to drop six of its intra-European flights.
"We can't get a slot in Frankfurt even after Delta relinquished a gaggle," Mr Ornstein says. "Deregulation is great on paper, but it has to be carried through in action as well."
It's not just smaller carriers that have problems. The powerful national airlines are wary of exploiting new freedoms such as flying in other domestic markets.
"It's too expensive,'' says Jean-Claude Baumgarten, a senior vice-president of Air France, arguing that it simply isn't profitable for the airline to open new domestic routes in other countries.
Even British Airways, which Mr Baumgarten says is the only European carrier with the financial muscle to buy existing airlines in other domestic markets, has had trouble making a go of it.
Neither TAT European Airways in France nor Deutsche BA in Germany, both of which BA bought four years ago, have yet shown a profit. They lost a combined pounds 68m in the most recent fiscal year.
Some of the big airlines point a finger at state aid. They say continuing handouts for state-owned carriers such as Air France, Spain's Iberia and Alitalia have kept capacity on the market that their competitors had hoped would have disappeared by now.
The problem is that many airlines are still saddled with costs more appropriate to the days of regulated markets and unionised workforces resistant to change.
Avmark International, a London consulting firm, estimates that costs at European airlines are about 40 per cent higher than those for their US competitors.
That translates directly into fares. American Express Travel estimates that prices in Europe are roughly double those in the US for flights of comparable distances.
About 64 per cent of routes within Europe are still operated by a single airline, and 30 per cent of routes are served by two airlines in an arrangement that consumer advocates dismiss as a duopoly. Only 6 per cent are served by at least three carriers, the European Commission estimates.
There are glimmers of hope, however. Around 80 new airlines have launched since 1993. Sixty have failed but the 20 that remain - as well as long- established smaller carriers such as Ireland's Ryan Air and Transswedde in Scandinavia - have begun making inroads into the big carriers' markets.
Britain's easyJet, founded by the Greek shipping heir Stelios Haji-Ioannou in late 1995, charges as little as pounds 58 for a round-trip ticket between London and Edinburgh - one-quarter the price of an unrestricted BA ticket.
Virgin Express undercuts rivals on its routes to Madrid, Rome and Barcelona by as much as 50 per cent. And Debonair Airways, based in London, charges pounds 230 for an unrestricted economy-class ticket between London and Copenhagen, almost half the price from BA, Air UK and SAS.
How? Debonair serves the route from Luton Airport where it is cheaper and easier for airlines to get runway access than at Heathrow or Gatwick.
Mr Haji-Ioannou says that easyJet, which began life with pounds 5m of start- up capital, fills about 70 per cent of its seats and expects to be profitable this year.
Chris Tarry, an analyst with Dresdner Kleinwort Benson, says that over time, the larger carriers such as BA and the start-ups like Virgin Express will settle into complementary roles.
The low-cost carriers will concentrate on short- and medium-haul routes, feeding passengers into hubs at which point the larger carriers can hook up to offer more lucrative long-haul routes, where they will concentrate their business.
And over the longer term, industry executives and analysts say, the face of European aviation should change substantially as inefficient carriers either reform themselves or are pushed out of the market.
Mr Ornstein of Virgin says: "We will definitely force a significant restructuring of aviation in Europe; consumers won't spend $1,000 to fly 400 miles anymore."