First-round voting for the 566 other constituencies - for voters who live in France - will take place on June 11. All run-off votes are scheduled for June 18.
Opinion polls predict Macron's centrist Republic On the Move (LREM) party will comfortably win a majority.
Having a majority in parliament is essential for Macron to be able to carry out his reforms plans, which include overhauling labor laws to favor business, cutting corporate tax, and investing 50 billion euros of public cash over five years in areas including job training and renewable energy.
Those 11 constituencies represent French citizens living in another country and are not necessarily typical of the broader French population. But they do chime with the overall majority for Macron that pollsters predict, though tilting even more towards LREM.
In most of those 10 foreign constituencies where they came first, Macron's candidates had well over 50 percent of the votes. However, turnout was too low for them to be elected without a run-off.
In the only one where LREM did not top the first round, it came second and its candidate is qualified for the two-way run-off.
The outgoing parliament had six left-wing representatives of French living abroad and five conservative and center-right ones. Macron's one-year old party did not exist then.