Recreational shooting can refer to several activities including hunting, participating in shooting competitions, or using firearms as a hobby. The laws surrounding firearms vary considerably between countries and bringing one nearly always involves some bureaucracy.
Legislation differs from one country to the next, but many countries are much more strict than e.g. USA.
The European Union, covering many European countries, has harmonized some of the legislation around bringing firearms. There is a European Firearm License ("firearms passport") meant to ease crossing borders inside the union with a firearm. In addition to the licence you need an invitation to a hunting or sport shooting event or similar documentation showing your need of the arm, a description of your coming participation and, for some countries, advance acceptance from the country in question. For carrying the firearm for other purposes you have to apply separately for permission (for a certain occasion or repeatedly), you may also need permission to get the firearm out of your country.
If you have a fire arms licence of a Nordic country and an invitation to a hunting or sport shooting event, you need no other paperwork to transport and use the weapon as allowed for local residents and needed for participating in the event. Without a Nordic permit you need licence and documentation in accordance with the EU regulations.
A firearm under transport must be unloaded and in an envelope. It must not be transported around needlessly. When stored, it must be in a place where not easily stolen, and additionally locked in or with some piece stored separately. Carrying the weapon for hunting is also regulated in the hunting law (you may e.g. not transport it in a motor vehicle in the terrain). You may not give the arm to anybody else, except someone else with the required licence or under your close supervision.
Hunting arms are restricted to certain types, with requirements varying by game. For hunting big game an (easy) shooting proficiency test is needed, unless you have documentation on a similar test or right to hunt similar game abroad.
Firearm regulation is regulated by law in France. All firearms have to be licensed and must have a unique identifier. Since the European Union creation, a European Firearm License has been created, allowing regulated and declared firearms to be transported cross-borders. An article about Firearms regulations from the Chateau de Janvry can be found here: How to Travel to France with Firearms.
In general Germany is a very restrictive country when it comes to firearms, however since the Weapons Act (Waffengesetz) was enacted on April 1, 2003 the regulations affecting hunters and recreational shooters have been significantly relaxed.
German law raised the minimum age for the purchase and possession of weapons from 16 to 18 for hunters, and 18 to 21 for marksmen.
Hunting is popular in Sweden, but regulated by both strict laws as well as local regulations. Also note that in Sweden you are never allowed to carry any kind of shooting weapon without a special permit, and failure to observe Swedish law in this case may incur severe fines, permanent confiscation of the weapon and possible imprisonment, as the carrying of a weapon without permit is considered a criminal offence.
If you have a fire arms permit of one Nordic country and an invitation to a hunting or sport shooting event, you need no other paperwork to carry the weapon as allowed for local residents.
Hunting and fishing are big business in Canada and they attract many tourists, especially from the US and Japan. Typically the companies that provide services to hunters can also help customers comply with Canadian laws. You need a hunting or fishing license and may also need a gun license.
Canadian weapons laws are considerably tighter than the US, and there is less variation between provinces than between US states.
- The Canadian Firearms Centre administers the gun regulations.
- Canada Customs have a page on import regulations.
A number of weapons are classed as prohibited. Getting a permit for these is generally impossible. Prohibited firearms include short-barrelled guns, fully-automatic weapons, rifles with collapsible stocks, and most 25 or 32 caliber pistols. Various other things are also prohibited — including mags with over 5 rounds for a long gun or 10 for a pistol, silencers, replicas such as Airsoft guns, switchblade knives, teargas or pepper spray.
There are also restricted weapons — any pistol that is not prohibited, M16 and AR-15, various others. Permits for these may be possible, but there is considerable bureaucracy to be dealt with.
The only weapon that would be relatively easy to import, or to rent, is one that is neither restricted nor prohibited, such as the typical hunter's rifle or shotgun. Even for that, there would be paperwork. There is no equivalent to the US second amendment in Canadian law; four-figure fines (or worse) for any undeclared firearm at Canadian customs are not uncommon.
Shooting sports such as hunting and competitive shooting are widely practiced. Rifle ranges often offer shooter safety and other classes for beginners.
Anyone who wishes to hunt must first purchase a hunting license valid for the state they will hunt in. Licenses are available at many rural stores or by mail/internet directly from the state. They are usually valid for a set period of time, or a set number of kills.
Foreigners on non-immigrant visas who wish to import guns for hunting or competitive shooting must file Form 6 NIA  with the Bureau of Alcohol, Tobacco and Firearms, as well as have a valid hunting license. Approval generally takes 6-8 weeks, so plan ahead.
It is only legal in the US for US citizens and legal permanent residents (green card holders) to purchase or own firearms without any special permit. Foreigner, who are illegally or unlawfully in the United States, are specifically prohibited from possessing any firearm or ammunition. Foreigners lawfully admitted to the United States under a non-immigrant visa may possess firearm if they are admitted to the United States for lawful hunting or sporting purposes or are in possession of a hunting license or permit lawfully issued in the United States. Another option is to borrow or rent guns from the shooting range of your choice to shoot on premises -- call ahead to see if this is an option.
Individual US States have a significant say over most of the regulations of firearms within their state. Travelers will want to check with individual states to make sure other restrictions will not apply to them. The pro-gun lobbyist organization, the National Rifle Association (Commonly referred to as the NRA)  provides an excellent service that explains most relevant state-by-state laws.