* Belgian tender for 34 warplanes worth about 3.5 bln euros
* France skips tender, offers bigger agreement
* Paris attempts to outdo U.S., British, Swedish offers (Adds details, quotes, background)
PARIS, Sept 7 (Reuters) - France on Thursday proposed a wide-ranging military deal with Belgium including the sale of Rafale fighter jets and going beyond the terms of the original Belgian tender.
The Rafales are made by France's Dassault Aviation , which is competing on the Belgian shortlist with Lockheed Martin, Boeing F-18, the British-led Eurofighter consortium and Sweden's Saab..
Belgium launched a tender in March to replace its ageing fleet of Lockheed Martin F-16 planes with 34 new fighters, in a deal that could be worth more than 3.5 billion euros ($4.2 billion).
But the French defence ministry said Paris was offering a partnership going well beyond the supply of equipment. It would include enhanced military cooperation between the two countries, training, and industrial and technical cooperation between companies from both NATO allies.
This would help strengthen European defence and its "strategic autonomy" at a time when it had never been more necessary, the ministry said.
A French official said Paris had offered the deal instead of responding to the tender offer, which closed earlier on Thursday. The Eurofighter consortium and Lockheed Martin submitted their bids earlier in the day, a source close to the matter said.
Dassault Aviation had no immediate comment, and the Belgian defence ministry said it would not comment until the process was finalised. The ministry said in March that a final decision was due to be made next year.
European Union leaders earlier this year launched their most ambitious defence plan for decades, agreeing a multi-billion-euro weapons fund and shared financing for battlegroups.
Tensions with Russia, a more inward-looking United States and Britain's decision to leave the EU have pushed European governments to confront years of division over military cooperation. They are also under pressure from U.S. President Donald Trump to shoulder more of the military and financial burden within NATO.
France struggled for years to secure its first foreign order for the Rafale but, since making a breakthrough with a 2015 deal to sell 24 of the planes to Egypt, it has notched up several other orders for the multi-role combat jet. It has since sold jets to Qatar and India, but has never been able to sell the plane in Europe.
($1 = 0.8330 euros) (Additional reporting by Cyril Altmeyer; Editing by Mark Trevelyan)