After investigating the rolls of Napoleon's Guard and infantry, I had another browse around the Mémoire des Hommes website of the Service Historique de la Défense, and took a look at the records of the French East India company, the Compagnie des Indes. The Company was originally created in 1664 as a rival to the British and Dutch companies. Like the HEIC, it couldn't help but meddle in local affairs, and the European conflicts between the two countries were also played out in India. The French got the worse of it, and the Compagnie virtually collapsed in 1764. It was revived in 1785, but was then abolished during the Revolution. Despite this, the French retained several enclaves in India, particularly around Pondicherry (now Puducherry) on the south-east coast, and Chandernagore (now Chandanaggar) until 1954 (yep, six years after the British left).
The approach is via the tab Présence française dans le monde. You are given several options. The Orientations historiques provides links to the municipal museum in Lorient, which is also the museum of the Compagnie, as well as to a number of other museums and academic institutions
The Compagnie's archives are held at Lorient, and the Archives du port de Lorient leads you to links to the inventories. Lorient itself was the main port for the company, having grown from the shipyard where the first company vessel was built.
If you know the name of a ship in which you are interested, then click on the Armement des navires link. This leads you to search screen, but the vessel name is a drop down menu, and covers vessels from L'Abeille, brigantine (one voyage from la Rochelle to Louisiana in 1721) to Le Zodiaque, 74 (one voyage from Lorient to India and the Mascarenas, then back to Brest in 1757-62), via captured vessels like the Little Dicky, a British merchantman captured by the Zodiaque's squadron off India. For each vessel, there is a reference to the piece number within the Archives of the ship's logs, and any correspondance from, or relating to, the vessel. Under the heading Activité et opérations is a link to a list of the Company's vessels, with the location of further archive material. Under the heading Personnel et passagers are links to any surviving muster rolls.
Equipages et passagers is one of the most interesting sections, because it provides links to the digitized muster rolls of each ship. So I returned to the trusty Dupont name and stuck that in the search form. To my utter, utter surprise, given the non-indexing indexes from elsewhere in this site, the search actually worked, and there are 127 Duponts. The first is actually a soldier, bound for Pondicherry, who boarded the Duc de Bourbon, 30, on 14 March 1741 and arrived on 24 August that same year. Clicking on the icon under Nom de navire takes you to the Armement des navires page, as above; clicking on the icon under pdf takes you to a pdf of the muster roll for that voyage.
The Duc de Bourbon was launched at Lorient on 6 May 1734, and made three voyages to the Indies, in 1736, 1740 and 1744, before being condemned at Pondicherry on 31 Oct 1746. During the last voyage, she had actually been condemned at Ile de France (the modern Mauritius) in 1744, but was commandeered and refitted by de la Bourdonnais as Le Bourbon, and served in his Indian campaign
For the 1741 voyage, she managed to cram 430 people on board - crew and passagers, including a draft of replacements for the garrison at Pondicherry, amongst whom no-first-name Dupont was numbered. For each man there is his name, his father's name, age, height and hair colour, town of origin, position on board and pay, manning depot and miscellaneous remarks (although these details are not scrupulously filled in for each individual). Perhaps unsurprisingly, the ship's company, from Captain Pierre Jazier de la Garde to fifteen-year-old landsman Thomas Aubert, all came either from Brittany or, to a lesser extent, Gascony. There is obviously some scope for these records to form the basis of research on manning the Company's ships.
There is little information about their passengers, however. We end up knowing nothing more about no-first-name Dupont or his comrades - neither their age nor their origins. What is striking, looking through the names, is the number of men who had nicknames, and that these nicknames became part of the official record - like Julien Ory known as Dent Cruelle, or Jean le Dun known as Rozette, or even (imagination having perhaps run low by now) Nicholas Morel known as Morel. ISTR from work I've done on other, non-military material, from the eighteenth century that such names, and their appearance in official records, were a feature of society generally at the time, and not just of army life. Incidentally, a number of users of the site have been complaining of having problems viewing some of the digitized records using Chrome and Explorer. So be warned. I've had no trouble using Firefox (he adds smugly).
Pictures: the waterfront at Pondicherry (from Wikipedia); a view of the port of Lorient (from the museum's website); Le Bourbon, serving under de la Bourdonnais (Wikipedia); a cross section through Le Massiac, indiaman (from the website of the museum).