When President Reagan addresses the European Parliament Wednesday, he will be greeted by the sight of Alex Falconer wearing outsize lapel badges proclaiming "Hands Off Nicaragua" and "No to Star Wars."

Falconer belongs to what many of his fellow deputies in Western Europe's first directly elected assembly regard as the "loony left." Things that most of his colleagues are for, he is against: the Atlantic Alliance, the European Community, even strengthening the powers of the Parliament of which he is a member.

And yet, almost despite his Scottish working-class roots and ideological blinkers, he has become noticeably more European in outlook in his 10 months as a Euro-MP (member of Parliament). His political disdain for the assembly has softened as a result of watching representatives of nations that waged wars against each other for centuries sitting down to squabble over the price of milk and pork.

"You see things in a different light when you come here. You understand that, although we may not have had a civil war in Britain since 1666-odd, these people have had civil wars all the time," he remarked in his strong Scottish brogue. "I don't like quoting Churchill, but it's definitely better to have jaw, jaw, jaw than war, war, war."

Derided by many as a "talking shop" with little real power, the European Parliament is a strange kind of political animal. Debates take place in seven languages simultaneously. The Parliament has been described as a "traveling circus," constantly moving from Strasbourg, where plenary sessions are held, to Luxemburg, where the 3,000-member secretariat is located, to Brussels, the site of committee meetings and party caucuses.

When the president wants to silence Falconer, as he did last Monday during a debate on whether President Reagan should be allowed to address the assembly, he simply cuts off his microphone. This tactic has an instant, almost miraculous effect. Without simultaneous interpretation, and knowing that deputies are unable to hear what is going on over their headphones, even the most articulate heckler falls silent.

Housed in a modern glass-and-concrete building overlooking one of Strasbourg's many canals, the Parliament reflects the state of Western Europe 40 years after the end of World War II. It is at once an immense bureaucratic factory producing resolutions and position papers that few people read, and an exciting cauldron of different nationalities and political traditions.

"If you sit in the chamber for an afternoon, you get a very vivid idea of the amazing diversity of European culture. You find out which nations speak with their arms, which with their legs, the style of their rhetoric, and their regard for facts," commented Katherina Fokke, the German leader of the socialist group, the largest political faction in the Parliament.

The Italian deputies are by common consent the most emotional, speaking in verbal flights of fantasy that may have nothing to do with the issue being discussed. The French pride themselves on the incontrovertible logic of their arguments and the elegance of their language.

The British are good humored, the Irish are folksy, and the Greeks are natural orators.

The Germans tend to produce streams of statistics along with an occasional display of angst. The Dutch and the Danes are the most earnest, littering their speeches with requests to their more excitable Latin colleagues to keep "both feet firmly planted on the ground."

The political spectrum ranges from neofascists to militant com- munists. Seated at the back are an odd assortment of environmentalists and radicals, including a good number of people who, in the phrase of Northern Ireland's Social Democratic and Labor Party leader John Hume, seem to be "wired up to the moon."

Recognizable European aspirations do seem to be emerging from this melting pot. "If you took the first three or four people you bumped into in front of the main railway stations of Europe, you would have a group very similar in composition to the present Parliament," said Altiero Spinelli, 78, an Italian ex-resistance fighter now regarded as one of the "fathers of Europe." "The encouraging thing is that these very average people begin to think like Europeans when you mix them together."

Pier Dankert, a Dane and former president of the Parliament, commented: "It's difficult even for the anti-Common Marketeers to sustain total opposition for very long if they want to function effectively. The simple fact of living together in a community of 10 different nations can force you to adopt European attitudes."

Many Euro-MPs resent what they regard as the lack of serious press attention.

According to Derek Prag, the leader of the British Conservative group, one of the few occasions when London's Fleet Street papers paid much attention to a debate in Strasbourg was when a German socialist demanded that the British should drive on the right hand side of the road like everyone else. The proposal was rejected -- the Parliament did not have the power to enforce it anyway -- but not before a sudden upsurge of anti-European chauvinism in Britain.

A row of equal dimensions was caused by a French deputy's call for the tatooing of identification numbers on all European cats and dogs, to the horror of British pet-lovers.

For the most part, parliamentary business is made up of more mundane items such as debating a fisheries agreement between the European Community and Madagascar or agonizing about the increase of youth unemployment.

The main prerogative of the Parliament is to approve the European Community budget. The Euro-MPs have twice rejected the budget outright as a protest against the way the community is being run -- the most recent occasion being in December.

At question time, an institution borrowed from the British Parliament at Westminster, Euro-MPs can harass and lobby members of the European Commission, a kind of federal government.

In national parliaments, the most important commodity is votes, since they make or topple governments. In Strasbourg, it is speaking time, which is distributed to the political groups in proportion to their size and then rationed out to individual deputies by the group leaders.

Euro-MPs are rarely allowed to speak for more than four or five minutes, with the result that debates are frequently livelier and more to the point than in national parliaments.

The parliament is gradually evolving its own traditions. Realizing that heckling is ineffective, members who want to interrupt a debate resort instead to the device of posing arcane points of order to attract the president's attention.

"There are enormous numbers of procedural objections and comparatively few jokes. Four out of five jokes don't translate into other languages," notes Francois Bordry, director of the press office.

Six years after the first direct European elections, the Parliament has reached a turning point. The pioneering spirit that characterized the first generation of Euro-MPs has largely disappeared and the parliament is searching for its proper role.

Proposals to extend the powers of the Parliament and a project for "political union" between different European countries will be discussed at a European summit next month. Next year, the Parliament will admit Spanish and Portuguese deputies, at the same time increasing the official languages to nine.

Dankert, the former president, said, "I sometimes wonder how long this can all be sustained. Decreasing public support means that political pressure for us to get more power is also decreasing. You cannot go on directly electing a talking shop."

A different view is taken by the present president, Pierre Pflimlin, a former mayor of Strasbourg who says that he has spent most of his life living in the "shadow of war":

"I am an optimist in the sense that up until now we have always been able to surmount our crises. It's true we spend a lot of time arguing about the price of butter -- but we argue about it as a family."