* Boeing set to launch 737 MAX 10 with flurry of orders
* Lockheed close to $37 bln-plus deal for F-35 warplane
* French President Macron gives boost to troubled A400M
By Tim Hepher and Mike Stone
PARIS, June 19 (Reuters) - The Paris Airshow opened under bright blue skies on Monday, with a new member of Boeing's best-selling 737 range set to vie for attention with a potentially huge order for F-35 fighter jets and a visit by French President Emmanuel Macron.
After years of booming orders, driven by rising air travel and more fuel-efficient planes, passenger jetmakers are bracing for a slowdown in demand while they focus on meeting tight delivery schedules and ambitious production targets.
But U.S. planemaker Boeing is expected to generate a fresh burst of activity at the world's biggest airshow by launching the 737 MAX 10 to plug a gap against European rival Airbus's A321neo.
Industry sources say the 190-230 seat plane could attract in the region of 150 orders at the July 19-25 Paris event.
Not to be outdone, Airbus is close to clinching a roughly $5 billion deal with low-cost carrier Viva Air Peru for about 30 planes, two industry sources said on Sunday.
While demand for passenger jets may be faltering, there are signs interest in military aircraft is picking up after years in the doldrums due to budget cuts and weak economic growth.
Lockheed Martin is in the final stages of negotiating a $37 billion-plus deal to sell 440 F-35 fighter jets to a group of 11 nations including the United States, two people familiar with the matter told Reuters.
That would be the biggest deal yet for the stealthy warplane, set to make its Paris Airshow debut this week.
In another boost for a defence project, French President Emmanuel Macron was due to fly into the show on an Airbus A400M military transporter in his first official engagement since winning a parliamentary majority in elections on Sunday.
His arrival is expected to be followed by a flypast by the world's largest passenger plane, the Airbus A380, and France's aerial display team.
The ceremony will lend high-level support to two ambitious European aerospace projects tarnished by problems in recent years: the A400M because of chronic cost overruns and delays and the A380 because of weak sales that threaten its future.
Airbus said on Sunday it was working on an upgrade of the A380 - called A380plus - with fuel-saving wingtips, confirming plans reported by Reuters in March.
Boeing, however, is expected to say at the Paris show that demand for mammoth planes such as the A380 and its own 747 is moribund. (Additional reporting by Vicki Bryan; writing by Mark Potter; editing by David Clarke)