Police briefly detained the protesters.
The envoy was questioned on Friday after his Indian wife alleged he sexually abused their three-year-old.
Although a case has been registered against him, he has not been arrested or formally charged. The envoy has made no public comment as yet.
Police say they are trying to confirm if the man has diplomatic immunity.
The wife of the envoy has written to the French ambassador in India and the Indian government, to prevent her husband from leaving the country until all legal proceedings are complete.
She has also asked the French Embassy for financial support for herself and her three children, who are French citizens.
The French Consulate-General in Bangalore confirmed that "a complaint had been lodged regarding the rape of a minor girl who is a French national".
"The complaint names the father of the child, who is a consular agent of this Consulate-General. An investigation is under way for which this Consulate-General is extending its full cooperation with the police and the authorities in charge," the Consulate said in a press release on Monday.
"It remains also in touch with the family of the child," it added.
The complaint was lodged on Thursday night, after the envoy's wife approached the Bangalore-based non-governmental organisation, Enfold India, for help.

Hertfordshire Police said it was looking for Aidan Chaves in connection with "an incident of affray" in Sawbridgeworth, Hertfordshire.
The game between Sawbridgeworth Town and Clapton FC on 25 March was abandoned.
It followed reports a player appeared to get a  knife out after being spat at by a Clapton fan.
Mr Chaves is believed to be in Hertfordshire.
Police said the 26-year-old also had connections to London.
The Essex Senior League match, taking place at Sawbridgeworth's Crofters End ground, was abandoned after 95 minutes.
Following the match Sawbridgeworth Town said a player's registration had been terminated.
A spokesman for the club said the player in question would "never represent" them again and had been given a life ban from the ground.
Clapton was declared the winner because the score stood as it was at 95 minutes Sawbridgeworth Town 0 - Clapton 1.

BBC Wiltshire report the 23-year-old forward left Sixfields before kick-off, having been told he wasn't involved in the squad for the League One match.
Head coach Luke Williams said the matter would be dealt with "in house".
The Robins are in the relegation zone after five straight losses, four points from safety, with 14 matches remaining.
Swindon have won three, drawn four and lost 11 of their 18 games in all competitions since Tim Sherwood's appointment as director of football on 10 November.

Yorkshire Water said the problem was detected at water treatment works at Tophill Low and Keldgate.
A spokesman said the issue had now been resolved but it could take several hours for water supplies to return to normal.
The HU7 and HU8 postcodes were particularly affected by the problem, along with other places in the city.
Tens of thousands of residents could be affected, but the exact figure will not be known until an investigation has been carried out.
Yorkshire Water said: "We apologise for the inconvenience caused this morning and hope to get the issue resolved and the water supply back to normal by the end of the day."
Demonstrations have been held outside the French consulate in the Indian city of Bangalore demanding the arrest of a French official accused of abusing his daughter.
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Swindon Town's Jermaine Hylton may face internal disciplinary action after walking out on his side before Tuesday's 2-1 loss at Northampton Town.
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Thousands of homes in Hull have been left without water due to a technical fault.