PARIS/LONDON, Sept 21 (Reuters) - French industrial group Schneider Electric said it would proceed with a full takeover of British software company Aveva Plc, offering 31 pounds per share in a deal valuing the whole of Aveva at around 9.48 billion pounds ($10.8 billion).

Schneider said its offer represented a premium of around 41% to Aveva's closing share price of 21.92 pounds on Aug. 23, before Schneider first stated its intentions to consider a full buyout.

Shares in Aveva rose 2.2% in early deals in London, while Schneider Electric was down 1%.

Schneider already owns nearly 60% of Aveva. It took majority control in 2017 in a reverse takeover that enabled the British company to retain its London listing. The French group paid 3 billion pounds at that time.

It said Aveva's software would remain "fully agnostic", meaning it will work with or without Schneider Electric hardware, and it would continue to be an autonomous business, with its workers not integrated into Schneider's teams.

The French company said this approach would keep Aveva's "specific culture as a software company". Aveva's products are used to design and manage oil rigs, ships and chemical plants, while the French multinational spans electrical components, energy management and industrial automation systems.

Analysts at Jefferies and Credit Suisse said the plan to keep the company agnostic and independent raised questions.

Jefferies said while it could see the industrial logic in areas such as the acceleration of software as a service and cost efficiencies, "we find the valuation expensive and need answers (as to) why it's not pursuing greater hardware integration".

Schneider added that any interim dividend of up to 13 pence would still be paid to Aveva shareholders without any reductions.

($1 = 0.8809 pounds) (Reporting by Benoit Van Overstraeten and Paul Sandle; Editing by GV De Clercq, Sudip Kar-Gupta and Jan Harvey)